KILLED proof of input_9k6VtvBxuj.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).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) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxWeightedTrs (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedTrs (9) CompletionProof [UPPER BOUND(ID), 0 ms] (10) CpxTypedWeightedCompleteTrs (11) NarrowingProof [BOTH BOUNDS(ID, ID), 199 ms] (12) CpxTypedWeightedCompleteTrs (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (14) CpxRNTS (15) InliningProof [UPPER BOUND(ID), 545 ms] (16) CpxRNTS (17) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (18) CpxRNTS (19) CompletionProof [UPPER BOUND(ID), 0 ms] (20) CpxTypedWeightedCompleteTrs (21) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 12 ms] (22) CpxRNTS (23) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (24) CdtProblem (25) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (26) CdtProblem (27) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (28) CdtProblem (29) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 10 ms] (30) CdtProblem (31) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (32) CdtProblem (33) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (34) CdtProblem (35) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (36) CdtProblem (37) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 18 ms] (38) CdtProblem (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (40) CdtProblem (41) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (42) CdtProblem (43) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (44) CdtProblem (45) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (46) CdtProblem (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (48) CdtProblem (49) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (50) CdtProblem (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (52) CdtProblem (53) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (54) CdtProblem (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (56) CdtProblem (57) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CdtProblem (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (60) CdtProblem (61) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CdtProblem (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (64) CdtProblem (65) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (66) CdtProblem (67) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 34 ms] (68) CdtProblem (69) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (70) CdtProblem (71) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (72) CdtProblem (73) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 19 ms] (78) CdtProblem (79) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 38 ms] (84) CdtProblem (85) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 2 ms] (86) CdtProblem (87) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 3 ms] (90) CdtProblem (91) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (94) CdtProblem (95) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 29 ms] (96) CdtProblem (97) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (98) CdtProblem (99) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 56 ms] (102) CdtProblem (103) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (106) CdtProblem (107) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 21 ms] (108) CdtProblem (109) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (110) CdtProblem (111) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 49 ms] (114) CdtProblem (115) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (116) CdtProblem (117) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (118) CdtProblem (119) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 44 ms] (120) CdtProblem (121) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (122) CdtProblem (123) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 78 ms] (126) CdtProblem (127) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (128) CdtProblem (129) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (130) CdtProblem (131) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 35 ms] (132) CdtProblem (133) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (134) CdtProblem (135) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 38 ms] (136) CdtProblem (137) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (138) CdtProblem (139) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 32 ms] (140) CdtProblem (141) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (142) CdtProblem (143) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 35 ms] (144) CdtProblem (145) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (146) CdtProblem (147) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 32 ms] (148) CdtProblem (149) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (150) CdtProblem (151) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 15 ms] (152) CdtProblem (153) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (154) CdtProblem (155) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (156) CdtProblem (157) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (158) CdtProblem (159) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 52 ms] (160) CdtProblem (161) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (162) CdtProblem (163) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (164) CdtProblem (165) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (166) CdtProblem (167) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 32 ms] (168) CdtProblem (169) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (170) CdtProblem (171) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 40 ms] (172) CdtProblem (173) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (174) CdtProblem (175) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 48 ms] (176) CdtProblem (177) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (178) CdtProblem (179) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (180) CdtProblem (181) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (182) CdtProblem (183) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 51 ms] (184) CdtProblem (185) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 10 ms] (186) CdtProblem (187) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (188) CdtProblem (189) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (190) CdtProblem (191) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 41 ms] (192) CdtProblem (193) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (194) CdtProblem (195) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 39 ms] (196) CdtProblem (197) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (198) CdtProblem (199) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 44 ms] (200) CdtProblem (201) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (202) CdtProblem (203) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 32 ms] (204) CdtProblem (205) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (206) CdtProblem (207) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 39 ms] (208) CdtProblem (209) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (210) 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, L) -> s(a__length(mark(L))) 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__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__length(nil) -> 0 a__length(cons(N, L)) -> a__U61(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))), L) 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)) -> a__U61(mark(X1), X2) mark(length(X)) -> a__length(mark(X)) 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) -> U61(X1, X2) a__length(X) -> length(X) 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, L) -> s(a__length(mark(L))) 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__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__length(nil) -> 0' a__length(cons(N, L)) -> a__U61(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))), L) 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)) -> a__U61(mark(X1), X2) mark(length(X)) -> a__length(mark(X)) 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) -> U61(X1, X2) a__length(X) -> length(X) 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, L) -> s(a__length(mark(L))) 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__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__length(nil) -> 0 a__length(cons(N, L)) -> a__U61(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))), L) 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)) -> a__U61(mark(X1), X2) mark(length(X)) -> a__length(mark(X)) 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) -> U61(X1, X2) a__length(X) -> length(X) 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) RelTrsToWeightedTrsProof (UPPER BOUND(ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (6) 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, L) -> s(a__length(mark(L))) [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__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__length(nil) -> 0 [1] a__length(cons(N, L)) -> a__U61(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))), L) [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)) -> a__U61(mark(X1), X2) [1] mark(length(X)) -> a__length(mark(X)) [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) -> U61(X1, X2) [1] a__length(X) -> length(X) [1] a__and(X1, X2) -> and(X1, X2) [1] a__isNatIListKind(X) -> isNatIListKind(X) [1] a__isNatKind(X) -> isNatKind(X) [1] Rewrite Strategy: INNERMOST ---------------------------------------- (7) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (8) 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, L) -> s(a__length(mark(L))) [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__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__length(nil) -> 0 [1] a__length(cons(N, L)) -> a__U61(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))), L) [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)) -> a__U61(mark(X1), X2) [1] mark(length(X)) -> a__length(mark(X)) [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) -> U61(X1, X2) [1] a__length(X) -> length(X) [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:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 cons :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 0 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 zeros :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U11 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 tt :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U12 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__isNatList :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U21 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U22 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__isNat :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U31 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U32 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U41 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U42 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U43 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__isNatIList :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U51 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U52 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U53 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U61 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 s :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__length :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 mark :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__and :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 length :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__isNatIListKind :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__isNatKind :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 isNatIListKind :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 nil :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 and :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 isNat :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 isNatKind :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U11 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U12 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 isNatList :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U21 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U22 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U31 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U32 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U41 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U42 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U43 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 isNatIList :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U51 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U52 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U53 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U61 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 Rewrite Strategy: INNERMOST ---------------------------------------- (9) 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__isNatKind_1 a__isNatList_1 a__isNatIListKind_1 a__isNatIList_1 a__U22_1 a__U53_1 a__U51_3 a__U41_3 a__U32_1 a__length_1 a__zeros a__U61_2 a__U11_2 a__U31_2 a__U42_2 a__U21_2 a__U12_1 a__U52_2 a__U43_1 Due to the following rules being added: none And the following fresh constants: none ---------------------------------------- (10) 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, L) -> s(a__length(mark(L))) [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__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__length(nil) -> 0 [1] a__length(cons(N, L)) -> a__U61(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))), L) [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)) -> a__U61(mark(X1), X2) [1] mark(length(X)) -> a__length(mark(X)) [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) -> U61(X1, X2) [1] a__length(X) -> length(X) [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:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 cons :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 0 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 zeros :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U11 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 tt :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U12 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__isNatList :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U21 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U22 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__isNat :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U31 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U32 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U41 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U42 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U43 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__isNatIList :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U51 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U52 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U53 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U61 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 s :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__length :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 mark :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__and :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 length :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__isNatIListKind :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__isNatKind :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 isNatIListKind :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 nil :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 and :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 isNat :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 isNatKind :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U11 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U12 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 isNatList :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U21 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U22 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U31 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U32 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U41 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U42 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U43 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 isNatIList :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U51 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U52 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U53 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U61 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 Rewrite Strategy: INNERMOST ---------------------------------------- (11) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (12) 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, V1) -> a__U12(isNatList(V1)) [2] a__U12(tt) -> tt [1] a__U21(tt, 0) -> a__U22(tt) [2] a__U21(tt, length(V1'')) -> a__U22(a__U11(a__isNatIListKind(V1''), V1'')) [2] a__U21(tt, s(V11)) -> a__U22(a__U21(a__isNatKind(V11), V11)) [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(V12, V2'')) -> a__U32(a__U51(a__and(a__isNatKind(V12), isNatIListKind(V2'')), V12, V2'')) [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(V13), V2) -> a__U42(a__U11(a__isNatIListKind(V13), V13), V2) [2] a__U41(tt, s(V14), V2) -> a__U42(a__U21(a__isNatKind(V14), V14), 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(V15, V21)) -> a__U43(a__U41(a__and(a__isNatKind(V15), isNatIListKind(V21)), V15, V21)) [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(V16), V2) -> a__U52(a__U11(a__isNatIListKind(V16), V16), V2) [2] a__U51(tt, s(V17), V2) -> a__U52(a__U21(a__isNatKind(V17), V17), 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(V18, V22)) -> a__U53(a__U51(a__and(a__isNatKind(V18), isNatIListKind(V22)), V18, V22)) [2] a__U52(tt, V2) -> a__U53(isNatList(V2)) [2] a__U53(tt) -> tt [1] a__U61(tt, L) -> s(a__length(mark(L))) [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(V19, V23))) -> a__U11(a__and(a__isNatKind(V19), isNatIListKind(V23)), cons(V19, V23)) [2] a__isNat(length(V1)) -> a__U11(isNatIListKind(V1), V1) [2] a__isNat(s(0)) -> a__U21(tt, 0) [2] a__isNat(s(length(V110))) -> a__U21(a__isNatIListKind(V110), length(V110)) [2] a__isNat(s(s(V111))) -> a__U21(a__isNatKind(V111), s(V111)) [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(V112, V24)) -> a__U31(a__and(a__isNatKind(V112), isNatIListKind(V24)), cons(V112, V24)) [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(V113), V2)) -> a__U41(a__and(a__isNatIListKind(V113), isNatIListKind(V2)), length(V113), V2) [2] a__isNatIList(cons(s(V114), V2)) -> a__U41(a__and(a__isNatKind(V114), isNatIListKind(V2)), s(V114), 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(V115), V2)) -> a__and(a__isNatIListKind(V115), isNatIListKind(V2)) [2] a__isNatIListKind(cons(s(V116), V2)) -> a__and(a__isNatKind(V116), isNatIListKind(V2)) [2] a__isNatIListKind(cons(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(V117), V2)) -> a__U51(a__and(a__isNatIListKind(V117), isNatIListKind(V2)), length(V117), V2) [2] a__isNatList(cons(s(V118), V2)) -> a__U51(a__and(a__isNatKind(V118), isNatIListKind(V2)), s(V118), V2) [2] a__isNatList(cons(V1, V2)) -> a__U51(a__and(isNatKind(V1), isNatIListKind(V2)), V1, V2) [2] a__length(nil) -> 0 [1] a__length(cons(N, nil)) -> a__U61(a__and(a__and(tt, isNatIListKind(nil)), and(isNat(N), isNatKind(N))), nil) [2] a__length(cons(N, cons(V119, V25))) -> a__U61(a__and(a__and(a__U51(a__and(a__isNatKind(V119), isNatIListKind(V25)), V119, V25), isNatIListKind(cons(V119, V25))), and(isNat(N), isNatKind(N))), cons(V119, V25)) [2] a__length(cons(N, L)) -> a__U61(a__and(a__and(isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))), L) [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)) -> a__U61(mark(X1), X2) [1] mark(length(X)) -> a__length(mark(X)) [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) -> U61(X1, X2) [1] a__length(X) -> length(X) [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:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 cons :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 0 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 zeros :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U11 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 tt :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U12 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__isNatList :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U21 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U22 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__isNat :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U31 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U32 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U41 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U42 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U43 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__isNatIList :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U51 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U52 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U53 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U61 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 s :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__length :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 mark :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__and :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 length :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__isNatIListKind :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__isNatKind :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 isNatIListKind :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 nil :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 and :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 isNat :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 isNatKind :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U11 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U12 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 isNatList :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U21 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U22 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U31 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U32 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U41 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U42 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U43 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 isNatIList :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U51 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U52 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U53 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U61 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 Rewrite Strategy: INNERMOST ---------------------------------------- (13) 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 ---------------------------------------- (14) Obligation: Complexity RNTS consisting of the following rules: 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(V11), V11)) :|: z = 2, V11 >= 0, z' = 1 + V11 a__U21(z, z') -{ 2 }-> a__U22(a__U11(a__isNatIListKind(V1''), V1'')) :|: z = 2, V1'' >= 0, z' = 1 + V1'' 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__U51(a__and(a__isNatKind(V12), 1 + V2''), V12, V2'')) :|: z = 2, V2'' >= 0, V12 >= 0, z' = 1 + V12 + V2'' 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(V14), V14), V2) :|: z = 2, V14 >= 0, V2 >= 0, z' = 1 + V14, z'' = V2 a__U41(z, z', z'') -{ 2 }-> a__U42(a__U11(a__isNatIListKind(V13), V13), V2) :|: z = 2, V13 >= 0, z' = 1 + V13, V2 >= 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(V15), 1 + V21), V15, V21)) :|: z = 2, z' = 1 + V15 + V21, V21 >= 0, V15 >= 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(V17), V17), V2) :|: z = 2, z' = 1 + V17, V2 >= 0, V17 >= 0, z'' = V2 a__U51(z, z', z'') -{ 2 }-> a__U52(a__U11(a__isNatIListKind(V16), V16), V2) :|: z = 2, z' = 1 + V16, V16 >= 0, 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__U51(a__and(a__isNatKind(V18), 1 + V22), V18, V22)) :|: z = 2, V18 >= 0, V22 >= 0, z' = 1 + V18 + V22 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') -{ 1 }-> 1 + a__length(mark(L)) :|: z = 2, L >= 0, z' = L a__U61(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 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(V111), 1 + V111) :|: z = 1 + (1 + V111), V111 >= 0 a__isNat(z) -{ 2 }-> a__U21(a__isNatIListKind(V110), 1 + V110) :|: V110 >= 0, z = 1 + (1 + V110) 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(V19), 1 + V23), 1 + V19 + V23) :|: V19 >= 0, V23 >= 0, z = 1 + (1 + V19 + V23) 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(V114), 1 + V2), 1 + V114, V2) :|: V114 >= 0, z = 1 + (1 + V114) + V2, V2 >= 0 a__isNatIList(z) -{ 2 }-> a__U41(a__and(a__isNatIListKind(V113), 1 + V2), 1 + V113, V2) :|: V2 >= 0, z = 1 + (1 + V113) + V2, V113 >= 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(V112), 1 + V24), 1 + V112 + V24) :|: z = 1 + V112 + V24, V24 >= 0, V112 >= 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(V116), 1 + V2) :|: z = 1 + (1 + V116) + V2, V2 >= 0, V116 >= 0 a__isNatIListKind(z) -{ 2 }-> a__and(a__isNatIListKind(V115), 1 + V2) :|: z = 1 + (1 + V115) + V2, V2 >= 0, V115 >= 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__U51(a__and(a__isNatKind(V118), 1 + V2), 1 + V118, V2) :|: V118 >= 0, z = 1 + (1 + V118) + V2, V2 >= 0 a__isNatList(z) -{ 2 }-> a__U51(a__and(a__isNatIListKind(V117), 1 + V2), 1 + V117, V2) :|: V117 >= 0, V2 >= 0, z = 1 + (1 + V117) + 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__U61(a__and(a__and(a__U51(a__and(a__isNatKind(V119), 1 + V25), V119, V25), 1 + (1 + V119 + V25)), 1 + (1 + N) + (1 + N)), 1 + V119 + V25) :|: z = 1 + N + (1 + V119 + V25), V25 >= 0, V119 >= 0, N >= 0 a__length(z) -{ 2 }-> a__U61(a__and(a__and(2, 1 + 1), 1 + (1 + N) + (1 + N)), 1) :|: z = 1 + N + 1, N >= 0 a__length(z) -{ 2 }-> a__U61(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__zeros -{ 1 }-> 3 :|: a__zeros -{ 1 }-> 1 + 0 + 3 :|: mark(z) -{ 1 }-> a__zeros :|: z = 3 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__U61(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 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 ---------------------------------------- (15) 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 ---------------------------------------- (16) Obligation: Complexity RNTS consisting of the following rules: 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(V11), V11)) :|: z = 2, V11 >= 0, z' = 1 + V11 a__U21(z, z') -{ 2 }-> a__U22(a__U11(a__isNatIListKind(V1''), V1'')) :|: z = 2, V1'' >= 0, z' = 1 + V1'' 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__U51(a__and(a__isNatKind(V12), 1 + V2''), V12, V2'')) :|: z = 2, V2'' >= 0, V12 >= 0, z' = 1 + V12 + V2'' 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(V14), V14), V2) :|: z = 2, V14 >= 0, V2 >= 0, z' = 1 + V14, z'' = V2 a__U41(z, z', z'') -{ 2 }-> a__U42(a__U11(a__isNatIListKind(V13), V13), V2) :|: z = 2, V13 >= 0, z' = 1 + V13, V2 >= 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(V15), 1 + V21), V15, V21)) :|: z = 2, z' = 1 + V15 + V21, V21 >= 0, V15 >= 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(V17), V17), V2) :|: z = 2, z' = 1 + V17, V2 >= 0, V17 >= 0, z'' = V2 a__U51(z, z', z'') -{ 2 }-> a__U52(a__U11(a__isNatIListKind(V16), V16), V2) :|: z = 2, z' = 1 + V16, V16 >= 0, 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__U51(a__and(a__isNatKind(V18), 1 + V22), V18, V22)) :|: z = 2, V18 >= 0, V22 >= 0, z' = 1 + V18 + V22 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') -{ 1 }-> 1 + a__length(mark(L)) :|: z = 2, L >= 0, z' = L a__U61(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 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(V111), 1 + V111) :|: z = 1 + (1 + V111), V111 >= 0 a__isNat(z) -{ 2 }-> a__U21(a__isNatIListKind(V110), 1 + V110) :|: V110 >= 0, z = 1 + (1 + V110) 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(V19), 1 + V23), 1 + V19 + V23) :|: V19 >= 0, V23 >= 0, z = 1 + (1 + V19 + V23) 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(V114), 1 + V2), 1 + V114, V2) :|: V114 >= 0, z = 1 + (1 + V114) + V2, V2 >= 0 a__isNatIList(z) -{ 2 }-> a__U41(a__and(a__isNatIListKind(V113), 1 + V2), 1 + V113, V2) :|: V2 >= 0, z = 1 + (1 + V113) + V2, V113 >= 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(V112), 1 + V24), 1 + V112 + V24) :|: z = 1 + V112 + V24, V24 >= 0, V112 >= 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(V116), 1 + V2) :|: z = 1 + (1 + V116) + V2, V2 >= 0, V116 >= 0 a__isNatIListKind(z) -{ 2 }-> a__and(a__isNatIListKind(V115), 1 + V2) :|: z = 1 + (1 + V115) + V2, V2 >= 0, V115 >= 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__U51(a__and(a__isNatKind(V118), 1 + V2), 1 + V118, V2) :|: V118 >= 0, z = 1 + (1 + V118) + V2, V2 >= 0 a__isNatList(z) -{ 2 }-> a__U51(a__and(a__isNatIListKind(V117), 1 + V2), 1 + V117, V2) :|: V117 >= 0, V2 >= 0, z = 1 + (1 + V117) + 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__U61(a__and(a__and(a__U51(a__and(a__isNatKind(V119), 1 + V25), V119, V25), 1 + (1 + V119 + V25)), 1 + (1 + N) + (1 + N)), 1 + V119 + V25) :|: z = 1 + N + (1 + V119 + V25), V25 >= 0, V119 >= 0, N >= 0 a__length(z) -{ 2 }-> a__U61(a__and(a__and(2, 1 + 1), 1 + (1 + N) + (1 + N)), 1) :|: z = 1 + N + 1, N >= 0 a__length(z) -{ 2 }-> a__U61(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__zeros -{ 1 }-> 3 :|: a__zeros -{ 1 }-> 1 + 0 + 3 :|: 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__U61(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 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 ---------------------------------------- (17) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (18) Obligation: Complexity RNTS consisting of the following rules: 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__U51(a__and(a__isNatKind(V12), 1 + V2''), V12, V2'')) :|: z = 2, V2'' >= 0, V12 >= 0, z' = 1 + V12 + V2'' 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' - 1 >= 0, z'' >= 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(V15), 1 + V21), V15, V21)) :|: z = 2, z' = 1 + V15 + V21, V21 >= 0, V15 >= 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'' >= 0, z' - 1 >= 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__U51(a__and(a__isNatKind(V18), 1 + V22), V18, V22)) :|: z = 2, V18 >= 0, V22 >= 0, z' = 1 + V18 + V22 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') -{ 1 }-> 1 + a__length(mark(z')) :|: z = 2, z' >= 0 a__U61(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 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(V19), 1 + V23), 1 + V19 + V23) :|: V19 >= 0, V23 >= 0, z = 1 + (1 + V19 + V23) 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(V114), 1 + V2), 1 + V114, V2) :|: V114 >= 0, z = 1 + (1 + V114) + V2, V2 >= 0 a__isNatIList(z) -{ 2 }-> a__U41(a__and(a__isNatIListKind(V113), 1 + V2), 1 + V113, V2) :|: V2 >= 0, z = 1 + (1 + V113) + V2, V113 >= 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(V112), 1 + V24), 1 + V112 + V24) :|: z = 1 + V112 + V24, V24 >= 0, V112 >= 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(V116), 1 + V2) :|: z = 1 + (1 + V116) + V2, V2 >= 0, V116 >= 0 a__isNatIListKind(z) -{ 2 }-> a__and(a__isNatIListKind(V115), 1 + V2) :|: z = 1 + (1 + V115) + V2, V2 >= 0, V115 >= 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__U51(a__and(a__isNatKind(V118), 1 + V2), 1 + V118, V2) :|: V118 >= 0, z = 1 + (1 + V118) + V2, V2 >= 0 a__isNatList(z) -{ 2 }-> a__U51(a__and(a__isNatIListKind(V117), 1 + V2), 1 + V117, V2) :|: V117 >= 0, V2 >= 0, z = 1 + (1 + V117) + 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__U61(a__and(a__and(a__U51(a__and(a__isNatKind(V119), 1 + V25), V119, V25), 1 + (1 + V119 + V25)), 1 + (1 + N) + (1 + N)), 1 + V119 + V25) :|: z = 1 + N + (1 + V119 + V25), V25 >= 0, V119 >= 0, N >= 0 a__length(z) -{ 2 }-> a__U61(a__and(a__and(2, 1 + 1), 1 + (1 + (z - 2)) + (1 + (z - 2))), 1) :|: z - 2 >= 0 a__length(z) -{ 2 }-> a__U61(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__zeros -{ 1 }-> 3 :|: a__zeros -{ 1 }-> 1 + 0 + 3 :|: 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__U61(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 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 ---------------------------------------- (19) 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 ---------------------------------------- (20) 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, L) -> s(a__length(mark(L))) [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__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__length(nil) -> 0 [1] a__length(cons(N, L)) -> a__U61(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))), L) [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)) -> a__U61(mark(X1), X2) [1] mark(length(X)) -> a__length(mark(X)) [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) -> U61(X1, X2) [1] a__length(X) -> length(X) [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:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 cons :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 0 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 zeros :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U11 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 tt :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U12 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__isNatList :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U21 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U22 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__isNat :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U31 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U32 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U41 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U42 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U43 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__isNatIList :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U51 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U52 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U53 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__U61 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 s :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__length :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 mark :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__and :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 length :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__isNatIListKind :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 a__isNatKind :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 isNatIListKind :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 nil :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 and :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 isNat :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 isNatKind :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U11 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U12 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 isNatList :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U21 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U22 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U31 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U32 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U41 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U42 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U43 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 isNatIList :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U51 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U52 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U53 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 U61 :: 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> 0:zeros:cons:tt:s:length:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 Rewrite Strategy: INNERMOST ---------------------------------------- (21) 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 ---------------------------------------- (22) 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') -{ 1 }-> 1 + a__length(mark(L)) :|: z = 2, L >= 0, z' = L a__U61(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 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__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__U61(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__zeros -{ 1 }-> 3 :|: a__zeros -{ 1 }-> 1 + 0 + 3 :|: mark(z) -{ 1 }-> a__zeros :|: z = 3 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__U61(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 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. ---------------------------------------- (23) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (24) 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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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) -> c26(A__LENGTH(mark(z0)), MARK(z0)) A__U61(z0, z1) -> c27 A__AND(tt, z0) -> c28(MARK(z0)) A__AND(z0, z1) -> c29 A__ISNAT(0) -> c30 A__ISNAT(length(z0)) -> c31(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c32(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNAT(z0) -> c33 A__ISNATILIST(z0) -> c34(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(zeros) -> c35 A__ISNATILIST(cons(z0, z1)) -> c36(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c37 A__ISNATILISTKIND(nil) -> c38 A__ISNATILISTKIND(zeros) -> c39 A__ISNATILISTKIND(cons(z0, z1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(z0) -> c41 A__ISNATKIND(0) -> c42 A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__ISNATKIND(z0) -> c45 A__ISNATLIST(nil) -> c46 A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(z0) -> c48 A__LENGTH(nil) -> c49 A__LENGTH(cons(z0, z1)) -> c50(A__U61(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) -> c51 MARK(zeros) -> c52(A__ZEROS) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c54(A__U12(mark(z0)), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0)) -> c57(A__U22(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U32(z0)) -> c60(A__U32(mark(z0)), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(U43(z0)) -> c63(A__U43(mark(z0)), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U53(z0)) -> c67(A__U53(mark(z0)), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(0) -> c74 MARK(tt) -> c75 MARK(s(z0)) -> c76(MARK(z0)) MARK(nil) -> c77 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) -> c26(A__LENGTH(mark(z0)), MARK(z0)) A__U61(z0, z1) -> c27 A__AND(tt, z0) -> c28(MARK(z0)) A__AND(z0, z1) -> c29 A__ISNAT(0) -> c30 A__ISNAT(length(z0)) -> c31(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c32(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNAT(z0) -> c33 A__ISNATILIST(z0) -> c34(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(zeros) -> c35 A__ISNATILIST(cons(z0, z1)) -> c36(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c37 A__ISNATILISTKIND(nil) -> c38 A__ISNATILISTKIND(zeros) -> c39 A__ISNATILISTKIND(cons(z0, z1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(z0) -> c41 A__ISNATKIND(0) -> c42 A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__ISNATKIND(z0) -> c45 A__ISNATLIST(nil) -> c46 A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(z0) -> c48 A__LENGTH(nil) -> c49 A__LENGTH(cons(z0, z1)) -> c50(A__U61(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) -> c51 MARK(zeros) -> c52(A__ZEROS) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c54(A__U12(mark(z0)), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0)) -> c57(A__U22(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U32(z0)) -> c60(A__U32(mark(z0)), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(U43(z0)) -> c63(A__U43(mark(z0)), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U53(z0)) -> c67(A__U53(mark(z0)), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(0) -> c74 MARK(tt) -> c75 MARK(s(z0)) -> c76(MARK(z0)) MARK(nil) -> c77 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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, 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_2, A__AND_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, 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_1, c29, c30, c31_2, c32_2, c33, c34_2, c35, c36_3, c37, c38, c39, c40_2, c41, c42, c43_1, c44_1, c45, c46, c47_3, c48, c49, c50_4, c51, c52_1, c53_2, c54_2, c55_1, c56_2, c57_2, c58_1, c59_2, c60_2, c61_2, c62_2, c63_2, c64_1, c65_2, c66_2, c67_2, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c74, c75, c76_1, c77 ---------------------------------------- (25) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 38 trailing nodes: A__ISNATILISTKIND(z0) -> c41 A__LENGTH(nil) -> c49 A__U11(z0, z1) -> c3 A__U53(tt) -> c24 A__U53(z0) -> c25 A__ZEROS -> c A__ISNATILIST(zeros) -> c35 A__U51(z0, z1, z2) -> c21 A__U12(tt) -> c4 MARK(zeros) -> c52(A__ZEROS) A__ISNATILIST(z0) -> c37 A__U12(z0) -> c5 A__ISNATLIST(z0) -> c48 A__U32(tt) -> c12 A__LENGTH(z0) -> c51 A__ISNATILISTKIND(nil) -> c38 A__ISNATLIST(nil) -> c46 A__ISNAT(z0) -> c33 A__ISNATKIND(0) -> c42 A__U61(z0, z1) -> c27 A__U22(tt) -> c8 A__U41(z0, z1, z2) -> c15 A__U31(z0, z1) -> c11 A__U42(z0, z1) -> c17 MARK(nil) -> c77 A__U43(z0) -> c19 A__ISNATILISTKIND(zeros) -> c39 A__U21(z0, z1) -> c7 A__ZEROS -> c1 A__ISNAT(0) -> c30 A__U52(z0, z1) -> c23 MARK(tt) -> c75 MARK(0) -> c74 A__ISNATKIND(z0) -> c45 A__AND(z0, z1) -> c29 A__U43(tt) -> c18 A__U32(z0) -> c13 A__U22(z0) -> c9 ---------------------------------------- (26) 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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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) -> c26(A__LENGTH(mark(z0)), MARK(z0)) A__AND(tt, z0) -> c28(MARK(z0)) A__ISNAT(length(z0)) -> c31(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c32(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c34(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c36(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)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c50(A__U61(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)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c54(A__U12(mark(z0)), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0)) -> c57(A__U22(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U32(z0)) -> c60(A__U32(mark(z0)), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(U43(z0)) -> c63(A__U43(mark(z0)), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U53(z0)) -> c67(A__U53(mark(z0)), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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) -> c26(A__LENGTH(mark(z0)), MARK(z0)) A__AND(tt, z0) -> c28(MARK(z0)) A__ISNAT(length(z0)) -> c31(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c32(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c34(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c36(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)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c50(A__U61(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)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c54(A__U12(mark(z0)), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0)) -> c57(A__U22(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U32(z0)) -> c60(A__U32(mark(z0)), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(U43(z0)) -> c63(A__U43(mark(z0)), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U53(z0)) -> c67(A__U53(mark(z0)), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, 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_2, A__AND_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, MARK_1 Compound Symbols: c2_2, c6_2, c10_2, c14_2, c16_2, c20_2, c22_2, c26_2, c28_1, c31_2, c32_2, c34_2, c36_3, c40_2, c43_1, c44_1, c47_3, c50_4, c53_2, c54_2, c55_1, c56_2, c57_2, c58_1, c59_2, c60_2, c61_2, c62_2, c63_2, c64_1, c65_2, c66_2, c67_2, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1 ---------------------------------------- (27) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 10 trailing tuple parts ---------------------------------------- (28) 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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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) -> c26(A__LENGTH(mark(z0)), MARK(z0)) A__AND(tt, z0) -> c28(MARK(z0)) A__ISNAT(length(z0)) -> c31(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c32(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c34(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c36(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)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c50(A__U61(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)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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) -> c26(A__LENGTH(mark(z0)), MARK(z0)) A__AND(tt, z0) -> c28(MARK(z0)) A__ISNAT(length(z0)) -> c31(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c32(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c34(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c36(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)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c50(A__U61(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)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__U41_3, A__U51_3, A__U61_2, A__AND_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2 Compound Symbols: c14_2, c20_2, c26_2, c28_1, c31_2, c32_2, c34_2, c36_3, c40_2, c43_1, c44_1, c47_3, c50_4, c53_2, c55_1, c56_2, c58_1, c59_2, c61_2, c62_2, c64_1, c65_2, c66_2, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1 ---------------------------------------- (29) 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)) ---------------------------------------- (30) 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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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) -> c26(A__LENGTH(mark(z0)), MARK(z0)) A__AND(tt, z0) -> c28(MARK(z0)) A__ISNAT(length(z0)) -> c31(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c32(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c34(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c36(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)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c50(A__U61(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)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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) -> c26(A__LENGTH(mark(z0)), MARK(z0)) A__AND(tt, z0) -> c28(MARK(z0)) A__ISNAT(length(z0)) -> c31(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c32(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c34(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c36(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)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c50(A__U61(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)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__U51_3, A__U61_2, A__AND_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3 Compound Symbols: c20_2, c26_2, c28_1, c31_2, c32_2, c34_2, c36_3, c40_2, c43_1, c44_1, c47_3, c50_4, c53_2, c55_1, c56_2, c58_1, c59_2, c61_2, c62_2, c64_1, c65_2, c66_2, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2 ---------------------------------------- (31) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (32) 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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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) -> c26(A__LENGTH(mark(z0)), MARK(z0)) A__AND(tt, z0) -> c28(MARK(z0)) A__ISNAT(length(z0)) -> c31(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c32(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c34(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c36(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)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c50(A__U61(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)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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) -> c26(A__LENGTH(mark(z0)), MARK(z0)) A__AND(tt, z0) -> c28(MARK(z0)) A__ISNAT(length(z0)) -> c31(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c32(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c34(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c36(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)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c50(A__U61(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)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__U51_3, A__U61_2, A__AND_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3 Compound Symbols: c20_2, c26_2, c28_1, c31_2, c32_2, c34_2, c36_3, c40_2, c43_1, c44_1, c47_3, c50_4, c53_2, c55_1, c56_2, c58_1, c59_2, c61_2, c62_2, c64_1, c65_2, c66_2, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1 ---------------------------------------- (33) 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)) ---------------------------------------- (34) 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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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) -> c26(A__LENGTH(mark(z0)), MARK(z0)) A__AND(tt, z0) -> c28(MARK(z0)) A__ISNAT(length(z0)) -> c31(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c32(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c34(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c36(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)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c50(A__U61(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)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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) -> c26(A__LENGTH(mark(z0)), MARK(z0)) A__AND(tt, z0) -> c28(MARK(z0)) A__ISNAT(length(z0)) -> c31(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c32(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c34(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c36(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)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c50(A__U61(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)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__U61_2, A__AND_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3 Compound Symbols: c26_2, c28_1, c31_2, c32_2, c34_2, c36_3, c40_2, c43_1, c44_1, c47_3, c50_4, c53_2, c55_1, c56_2, c58_1, c59_2, c61_2, c62_2, c64_1, c65_2, c66_2, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2 ---------------------------------------- (35) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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) -> c26(A__LENGTH(mark(z0)), MARK(z0)) A__AND(tt, z0) -> c28(MARK(z0)) A__ISNAT(length(z0)) -> c31(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c32(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c34(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c36(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)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c50(A__U61(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)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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) -> c26(A__LENGTH(mark(z0)), MARK(z0)) A__AND(tt, z0) -> c28(MARK(z0)) A__ISNAT(length(z0)) -> c31(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c32(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c34(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c36(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)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c50(A__U61(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)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__U61_2, A__AND_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3 Compound Symbols: c26_2, c28_1, c31_2, c32_2, c34_2, c36_3, c40_2, c43_1, c44_1, c47_3, c50_4, c53_2, c55_1, c56_2, c58_1, c59_2, c61_2, c62_2, c64_1, c65_2, c66_2, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1 ---------------------------------------- (37) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U61(tt, z0) -> c26(A__LENGTH(mark(z0)), MARK(z0)) by A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros), MARK(zeros)) A__U61(tt, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, 0) -> c26(A__LENGTH(0), MARK(0)) A__U61(tt, tt) -> c26(A__LENGTH(tt), MARK(tt)) A__U61(tt, s(z0)) -> c26(A__LENGTH(s(mark(z0))), MARK(s(z0))) A__U61(tt, nil) -> c26(A__LENGTH(nil), MARK(nil)) ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNAT(length(z0)) -> c31(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c32(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c34(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c36(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)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c50(A__U61(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)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, zeros) -> c26(A__LENGTH(a__zeros), MARK(zeros)) A__U61(tt, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, 0) -> c26(A__LENGTH(0), MARK(0)) A__U61(tt, tt) -> c26(A__LENGTH(tt), MARK(tt)) A__U61(tt, s(z0)) -> c26(A__LENGTH(s(mark(z0))), MARK(s(z0))) A__U61(tt, nil) -> c26(A__LENGTH(nil), MARK(nil)) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNAT(length(z0)) -> c31(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c32(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c34(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c36(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)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c50(A__U61(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)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, zeros) -> c26(A__LENGTH(a__zeros), MARK(zeros)) A__U61(tt, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, 0) -> c26(A__LENGTH(0), MARK(0)) A__U61(tt, tt) -> c26(A__LENGTH(tt), MARK(tt)) A__U61(tt, s(z0)) -> c26(A__LENGTH(s(mark(z0))), MARK(s(z0))) A__U61(tt, nil) -> c26(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2 Compound Symbols: c28_1, c31_2, c32_2, c34_2, c36_3, c40_2, c43_1, c44_1, c47_3, c50_4, c53_2, c55_1, c56_2, c58_1, c59_2, c61_2, c62_2, c64_1, c65_2, c66_2, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2 ---------------------------------------- (39) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: A__U61(tt, nil) -> c26(A__LENGTH(nil), MARK(nil)) A__U61(tt, tt) -> c26(A__LENGTH(tt), MARK(tt)) A__U61(tt, 0) -> c26(A__LENGTH(0), MARK(0)) ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNAT(length(z0)) -> c31(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c32(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c34(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c36(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)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c50(A__U61(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)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, zeros) -> c26(A__LENGTH(a__zeros), MARK(zeros)) A__U61(tt, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, s(z0)) -> c26(A__LENGTH(s(mark(z0))), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNAT(length(z0)) -> c31(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c32(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c34(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c36(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)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c50(A__U61(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)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, zeros) -> c26(A__LENGTH(a__zeros), MARK(zeros)) A__U61(tt, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, s(z0)) -> c26(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2 Compound Symbols: c28_1, c31_2, c32_2, c34_2, c36_3, c40_2, c43_1, c44_1, c47_3, c50_4, c53_2, c55_1, c56_2, c58_1, c59_2, c61_2, c62_2, c64_1, c65_2, c66_2, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2 ---------------------------------------- (41) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (42) 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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNAT(length(z0)) -> c31(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c32(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c34(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c36(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)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c50(A__U61(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)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNAT(length(z0)) -> c31(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c32(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c34(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c36(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)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c50(A__U61(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)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2 Compound Symbols: c28_1, c31_2, c32_2, c34_2, c36_3, c40_2, c43_1, c44_1, c47_3, c50_4, c53_2, c55_1, c56_2, c58_1, c59_2, c61_2, c62_2, c64_1, c65_2, c66_2, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1 ---------------------------------------- (43) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ISNAT(length(z0)) -> c31(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) by A__ISNAT(length(nil)) -> c31(A__U11(tt, nil), A__ISNATILISTKIND(nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros), A__ISNATILISTKIND(zeros)) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(z0)) -> c31(A__U11(isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) ---------------------------------------- (44) 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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNAT(s(z0)) -> c32(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c34(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c36(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)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c50(A__U61(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)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil), A__ISNATILISTKIND(nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros), A__ISNATILISTKIND(zeros)) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(z0)) -> c31(A__U11(isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNAT(s(z0)) -> c32(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c34(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c36(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)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c50(A__U61(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)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil), A__ISNATILISTKIND(nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros), A__ISNATILISTKIND(zeros)) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(z0)) -> c31(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2 Compound Symbols: c28_1, c32_2, c34_2, c36_3, c40_2, c43_1, c44_1, c47_3, c50_4, c53_2, c55_1, c56_2, c58_1, c59_2, c61_2, c62_2, c64_1, c65_2, c66_2, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2 ---------------------------------------- (45) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (46) 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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNAT(s(z0)) -> c32(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c34(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c36(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)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c50(A__U61(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)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNAT(s(z0)) -> c32(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c34(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c36(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)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c50(A__U61(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)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2 Compound Symbols: c28_1, c32_2, c34_2, c36_3, c40_2, c43_1, c44_1, c47_3, c50_4, c53_2, c55_1, c56_2, c58_1, c59_2, c61_2, c62_2, c64_1, c65_2, c66_2, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1 ---------------------------------------- (47) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ISNAT(s(z0)) -> c32(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) by A__ISNAT(s(0)) -> c32(A__U21(tt, 0), A__ISNATKIND(0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(z0)) -> c32(A__U21(isNatKind(z0), z0), A__ISNATKIND(z0)) ---------------------------------------- (48) 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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATILIST(z0) -> c34(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c36(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)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c50(A__U61(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)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(0)) -> c32(A__U21(tt, 0), A__ISNATKIND(0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(z0)) -> c32(A__U21(isNatKind(z0), z0), A__ISNATKIND(z0)) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATILIST(z0) -> c34(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c36(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)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c50(A__U61(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)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(0)) -> c32(A__U21(tt, 0), A__ISNATKIND(0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(z0)) -> c32(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1 Compound Symbols: c28_1, c34_2, c36_3, c40_2, c43_1, c44_1, c47_3, c50_4, c53_2, c55_1, c56_2, c58_1, c59_2, c61_2, c62_2, c64_1, c65_2, c66_2, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2 ---------------------------------------- (49) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (50) 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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATILIST(z0) -> c34(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c36(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)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c50(A__U61(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)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATILIST(z0) -> c34(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c36(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)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c50(A__U61(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)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1 Compound Symbols: c28_1, c34_2, c36_3, c40_2, c43_1, c44_1, c47_3, c50_4, c53_2, c55_1, c56_2, c58_1, c59_2, c61_2, c62_2, c64_1, c65_2, c66_2, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1 ---------------------------------------- (51) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ISNATILIST(z0) -> c34(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) by A__ISNATILIST(nil) -> c34(A__U31(tt, nil), A__ISNATILISTKIND(nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros), A__ISNATILISTKIND(zeros)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(z0) -> c34(A__U31(isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) ---------------------------------------- (52) 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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATILIST(cons(z0, z1)) -> c36(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)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c50(A__U61(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)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(nil) -> c34(A__U31(tt, nil), A__ISNATILISTKIND(nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros), A__ISNATILISTKIND(zeros)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(z0) -> c34(A__U31(isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATILIST(cons(z0, z1)) -> c36(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)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c50(A__U61(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)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(nil) -> c34(A__U31(tt, nil), A__ISNATILISTKIND(nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros), A__ISNATILISTKIND(zeros)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(z0) -> c34(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1 Compound Symbols: c28_1, c36_3, c40_2, c43_1, c44_1, c47_3, c50_4, c53_2, c55_1, c56_2, c58_1, c59_2, c61_2, c62_2, c64_1, c65_2, c66_2, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2 ---------------------------------------- (53) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (54) 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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATILIST(cons(z0, z1)) -> c36(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)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c50(A__U61(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)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATILIST(cons(z0, z1)) -> c36(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)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c50(A__U61(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)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1 Compound Symbols: c28_1, c36_3, c40_2, c43_1, c44_1, c47_3, c50_4, c53_2, c55_1, c56_2, c58_1, c59_2, c61_2, c62_2, c64_1, c65_2, c66_2, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1 ---------------------------------------- (55) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ISNATILIST(cons(z0, z1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) ---------------------------------------- (56) 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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c50(A__U61(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)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c50(A__U61(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)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1 Compound Symbols: c28_1, c40_2, c43_1, c44_1, c47_3, c50_4, c53_2, c55_1, c56_2, c58_1, c59_2, c61_2, c62_2, c64_1, c65_2, c66_2, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3 ---------------------------------------- (57) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (58) 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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c50(A__U61(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)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c50(A__U61(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)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1 Compound Symbols: c28_1, c40_2, c43_1, c44_1, c47_3, c50_4, c53_2, c55_1, c56_2, c58_1, c59_2, c61_2, c62_2, c64_1, c65_2, c66_2, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2 ---------------------------------------- (59) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ISNATILISTKIND(cons(z0, z1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) by A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1)), A__ISNATKIND(0)) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__AND(isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) ---------------------------------------- (60) 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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c50(A__U61(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)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1)), A__ISNATKIND(0)) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__AND(isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c50(A__U61(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)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1)), A__ISNATKIND(0)) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1 Compound Symbols: c28_1, c43_1, c44_1, c47_3, c50_4, c53_2, c55_1, c56_2, c58_1, c59_2, c61_2, c62_2, c64_1, c65_2, c66_2, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2 ---------------------------------------- (61) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (62) 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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c50(A__U61(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)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c50(A__U61(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)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1 Compound Symbols: c28_1, c43_1, c44_1, c47_3, c50_4, c53_2, c55_1, c56_2, c58_1, c59_2, c61_2, c62_2, c64_1, c65_2, c66_2, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1 ---------------------------------------- (63) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ISNATLIST(cons(z0, z1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c50(A__U61(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)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c50(A__U61(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)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, A__LENGTH_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1 Compound Symbols: c28_1, c43_1, c44_1, c50_4, c53_2, c55_1, c56_2, c58_1, c59_2, c61_2, c62_2, c64_1, c65_2, c66_2, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3 ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c50(A__U61(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)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c50(A__U61(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)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, A__LENGTH_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1 Compound Symbols: c28_1, c43_1, c44_1, c50_4, c53_2, c55_1, c56_2, c58_1, c59_2, c61_2, c62_2, c64_1, c65_2, c66_2, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2 ---------------------------------------- (67) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__LENGTH(cons(z0, z1)) -> c50(A__U61(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)) -> c50(A__U61(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)) -> c50(A__U61(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)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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)) -> c50(A__U61(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)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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)) -> c50(A__U61(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)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c53_2, c55_1, c56_2, c58_1, c59_2, c61_2, c62_2, c64_1, c65_2, c66_2, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4 ---------------------------------------- (69) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c53_2, c55_1, c56_2, c58_1, c59_2, c61_2, c62_2, c64_1, c65_2, c66_2, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2 ---------------------------------------- (71) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) by MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1), MARK(zeros)) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(cons(z0, z1), x1)) -> c53(A__U11(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U11(0, x1)) -> c53(A__U11(0, x1), MARK(0)) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1), MARK(tt)) MARK(U11(s(z0), x1)) -> c53(A__U11(s(mark(z0)), x1), MARK(s(z0))) MARK(U11(nil, x1)) -> c53(A__U11(nil, x1), MARK(nil)) ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1), MARK(zeros)) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(cons(z0, z1), x1)) -> c53(A__U11(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U11(0, x1)) -> c53(A__U11(0, x1), MARK(0)) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1), MARK(tt)) MARK(U11(s(z0), x1)) -> c53(A__U11(s(mark(z0)), x1), MARK(s(z0))) MARK(U11(nil, x1)) -> c53(A__U11(nil, x1), MARK(nil)) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1), MARK(zeros)) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(cons(z0, z1), x1)) -> c53(A__U11(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U11(0, x1)) -> c53(A__U11(0, x1), MARK(0)) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1), MARK(tt)) MARK(U11(s(z0), x1)) -> c53(A__U11(s(mark(z0)), x1), MARK(s(z0))) MARK(U11(nil, x1)) -> c53(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c56_2, c58_1, c59_2, c61_2, c62_2, c64_1, c65_2, c66_2, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2 ---------------------------------------- (73) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(U11(nil, x1)) -> c53(A__U11(nil, x1), MARK(nil)) MARK(U11(0, x1)) -> c53(A__U11(0, x1), MARK(0)) ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1), MARK(zeros)) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(cons(z0, z1), x1)) -> c53(A__U11(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1), MARK(tt)) MARK(U11(s(z0), x1)) -> c53(A__U11(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1), MARK(zeros)) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(cons(z0, z1), x1)) -> c53(A__U11(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1), MARK(tt)) MARK(U11(s(z0), x1)) -> c53(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c56_2, c58_1, c59_2, c61_2, c62_2, c64_1, c65_2, c66_2, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2 ---------------------------------------- (75) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c56_2, c58_1, c59_2, c61_2, c62_2, c64_1, c65_2, c66_2, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1 ---------------------------------------- (77) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) by MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1), MARK(zeros)) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(cons(z0, z1), x1)) -> c56(A__U21(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U21(0, x1)) -> c56(A__U21(0, x1), MARK(0)) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1), MARK(tt)) MARK(U21(s(z0), x1)) -> c56(A__U21(s(mark(z0)), x1), MARK(s(z0))) MARK(U21(nil, x1)) -> c56(A__U21(nil, x1), MARK(nil)) ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1), MARK(zeros)) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(cons(z0, z1), x1)) -> c56(A__U21(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U21(0, x1)) -> c56(A__U21(0, x1), MARK(0)) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1), MARK(tt)) MARK(U21(s(z0), x1)) -> c56(A__U21(s(mark(z0)), x1), MARK(s(z0))) MARK(U21(nil, x1)) -> c56(A__U21(nil, x1), MARK(nil)) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1), MARK(zeros)) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(cons(z0, z1), x1)) -> c56(A__U21(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U21(0, x1)) -> c56(A__U21(0, x1), MARK(0)) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1), MARK(tt)) MARK(U21(s(z0), x1)) -> c56(A__U21(s(mark(z0)), x1), MARK(s(z0))) MARK(U21(nil, x1)) -> c56(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c59_2, c61_2, c62_2, c64_1, c65_2, c66_2, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2 ---------------------------------------- (79) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(U21(0, x1)) -> c56(A__U21(0, x1), MARK(0)) MARK(U21(nil, x1)) -> c56(A__U21(nil, x1), MARK(nil)) ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1), MARK(zeros)) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(cons(z0, z1), x1)) -> c56(A__U21(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1), MARK(tt)) MARK(U21(s(z0), x1)) -> c56(A__U21(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1), MARK(zeros)) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(cons(z0, z1), x1)) -> c56(A__U21(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1), MARK(tt)) MARK(U21(s(z0), x1)) -> c56(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c59_2, c61_2, c62_2, c64_1, c65_2, c66_2, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2 ---------------------------------------- (81) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c59_2, c61_2, c62_2, c64_1, c65_2, c66_2, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1 ---------------------------------------- (83) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) by MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1), MARK(zeros)) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(cons(z0, z1), x1)) -> c59(A__U31(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U31(0, x1)) -> c59(A__U31(0, x1), MARK(0)) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1), MARK(tt)) MARK(U31(s(z0), x1)) -> c59(A__U31(s(mark(z0)), x1), MARK(s(z0))) MARK(U31(nil, x1)) -> c59(A__U31(nil, x1), MARK(nil)) ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1), MARK(zeros)) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(cons(z0, z1), x1)) -> c59(A__U31(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U31(0, x1)) -> c59(A__U31(0, x1), MARK(0)) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1), MARK(tt)) MARK(U31(s(z0), x1)) -> c59(A__U31(s(mark(z0)), x1), MARK(s(z0))) MARK(U31(nil, x1)) -> c59(A__U31(nil, x1), MARK(nil)) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1), MARK(zeros)) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(cons(z0, z1), x1)) -> c59(A__U31(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U31(0, x1)) -> c59(A__U31(0, x1), MARK(0)) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1), MARK(tt)) MARK(U31(s(z0), x1)) -> c59(A__U31(s(mark(z0)), x1), MARK(s(z0))) MARK(U31(nil, x1)) -> c59(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c61_2, c62_2, c64_1, c65_2, c66_2, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2 ---------------------------------------- (85) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(U31(nil, x1)) -> c59(A__U31(nil, x1), MARK(nil)) MARK(U31(0, x1)) -> c59(A__U31(0, x1), MARK(0)) ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1), MARK(zeros)) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(cons(z0, z1), x1)) -> c59(A__U31(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1), MARK(tt)) MARK(U31(s(z0), x1)) -> c59(A__U31(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1), MARK(zeros)) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(cons(z0, z1), x1)) -> c59(A__U31(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1), MARK(tt)) MARK(U31(s(z0), x1)) -> c59(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c61_2, c62_2, c64_1, c65_2, c66_2, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2 ---------------------------------------- (87) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c61_2, c62_2, c64_1, c65_2, c66_2, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1 ---------------------------------------- (89) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) by MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2), MARK(zeros)) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(cons(z0, z1), x1, x2)) -> c61(A__U41(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1))) MARK(U41(0, x1, x2)) -> c61(A__U41(0, x1, x2), MARK(0)) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2), MARK(tt)) MARK(U41(s(z0), x1, x2)) -> c61(A__U41(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U41(nil, x1, x2)) -> c61(A__U41(nil, x1, x2), MARK(nil)) ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2), MARK(zeros)) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(cons(z0, z1), x1, x2)) -> c61(A__U41(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1))) MARK(U41(0, x1, x2)) -> c61(A__U41(0, x1, x2), MARK(0)) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2), MARK(tt)) MARK(U41(s(z0), x1, x2)) -> c61(A__U41(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U41(nil, x1, x2)) -> c61(A__U41(nil, x1, x2), MARK(nil)) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2), MARK(zeros)) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(cons(z0, z1), x1, x2)) -> c61(A__U41(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1))) MARK(U41(0, x1, x2)) -> c61(A__U41(0, x1, x2), MARK(0)) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2), MARK(tt)) MARK(U41(s(z0), x1, x2)) -> c61(A__U41(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U41(nil, x1, x2)) -> c61(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c62_2, c64_1, c65_2, c66_2, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2 ---------------------------------------- (91) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(U41(nil, x1, x2)) -> c61(A__U41(nil, x1, x2), MARK(nil)) MARK(U41(0, x1, x2)) -> c61(A__U41(0, x1, x2), MARK(0)) ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2), MARK(zeros)) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(cons(z0, z1), x1, x2)) -> c61(A__U41(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2), MARK(tt)) MARK(U41(s(z0), x1, x2)) -> c61(A__U41(s(mark(z0)), x1, x2), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2), MARK(zeros)) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(cons(z0, z1), x1, x2)) -> c61(A__U41(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2), MARK(tt)) MARK(U41(s(z0), x1, x2)) -> c61(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c62_2, c64_1, c65_2, c66_2, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2 ---------------------------------------- (93) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c62_2, c64_1, c65_2, c66_2, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1 ---------------------------------------- (95) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) by MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1), MARK(zeros)) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(cons(z0, z1), x1)) -> c62(A__U42(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U42(0, x1)) -> c62(A__U42(0, x1), MARK(0)) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1), MARK(tt)) MARK(U42(s(z0), x1)) -> c62(A__U42(s(mark(z0)), x1), MARK(s(z0))) MARK(U42(nil, x1)) -> c62(A__U42(nil, x1), MARK(nil)) ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1), MARK(zeros)) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(cons(z0, z1), x1)) -> c62(A__U42(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U42(0, x1)) -> c62(A__U42(0, x1), MARK(0)) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1), MARK(tt)) MARK(U42(s(z0), x1)) -> c62(A__U42(s(mark(z0)), x1), MARK(s(z0))) MARK(U42(nil, x1)) -> c62(A__U42(nil, x1), MARK(nil)) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1), MARK(zeros)) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(cons(z0, z1), x1)) -> c62(A__U42(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U42(0, x1)) -> c62(A__U42(0, x1), MARK(0)) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1), MARK(tt)) MARK(U42(s(z0), x1)) -> c62(A__U42(s(mark(z0)), x1), MARK(s(z0))) MARK(U42(nil, x1)) -> c62(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c65_2, c66_2, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2 ---------------------------------------- (97) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(U42(nil, x1)) -> c62(A__U42(nil, x1), MARK(nil)) MARK(U42(0, x1)) -> c62(A__U42(0, x1), MARK(0)) ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1), MARK(zeros)) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(cons(z0, z1), x1)) -> c62(A__U42(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1), MARK(tt)) MARK(U42(s(z0), x1)) -> c62(A__U42(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1), MARK(zeros)) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(cons(z0, z1), x1)) -> c62(A__U42(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1), MARK(tt)) MARK(U42(s(z0), x1)) -> c62(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c65_2, c66_2, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2 ---------------------------------------- (99) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c65_2, c66_2, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1 ---------------------------------------- (101) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) by MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2), MARK(zeros)) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(cons(z0, z1), x1, x2)) -> c65(A__U51(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1))) MARK(U51(0, x1, x2)) -> c65(A__U51(0, x1, x2), MARK(0)) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2), MARK(tt)) MARK(U51(s(z0), x1, x2)) -> c65(A__U51(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U51(nil, x1, x2)) -> c65(A__U51(nil, x1, x2), MARK(nil)) ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2), MARK(zeros)) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(cons(z0, z1), x1, x2)) -> c65(A__U51(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1))) MARK(U51(0, x1, x2)) -> c65(A__U51(0, x1, x2), MARK(0)) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2), MARK(tt)) MARK(U51(s(z0), x1, x2)) -> c65(A__U51(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U51(nil, x1, x2)) -> c65(A__U51(nil, x1, x2), MARK(nil)) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2), MARK(zeros)) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(cons(z0, z1), x1, x2)) -> c65(A__U51(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1))) MARK(U51(0, x1, x2)) -> c65(A__U51(0, x1, x2), MARK(0)) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2), MARK(tt)) MARK(U51(s(z0), x1, x2)) -> c65(A__U51(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U51(nil, x1, x2)) -> c65(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c66_2, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2 ---------------------------------------- (103) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(U51(0, x1, x2)) -> c65(A__U51(0, x1, x2), MARK(0)) MARK(U51(nil, x1, x2)) -> c65(A__U51(nil, x1, x2), MARK(nil)) ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2), MARK(zeros)) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(cons(z0, z1), x1, x2)) -> c65(A__U51(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2), MARK(tt)) MARK(U51(s(z0), x1, x2)) -> c65(A__U51(s(mark(z0)), x1, x2), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2), MARK(zeros)) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(cons(z0, z1), x1, x2)) -> c65(A__U51(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2), MARK(tt)) MARK(U51(s(z0), x1, x2)) -> c65(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c66_2, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2 ---------------------------------------- (105) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c66_2, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1 ---------------------------------------- (107) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) by MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1), MARK(zeros)) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(cons(z0, z1), x1)) -> c66(A__U52(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U52(0, x1)) -> c66(A__U52(0, x1), MARK(0)) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1), MARK(tt)) MARK(U52(s(z0), x1)) -> c66(A__U52(s(mark(z0)), x1), MARK(s(z0))) MARK(U52(nil, x1)) -> c66(A__U52(nil, x1), MARK(nil)) ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1), MARK(zeros)) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(cons(z0, z1), x1)) -> c66(A__U52(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U52(0, x1)) -> c66(A__U52(0, x1), MARK(0)) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1), MARK(tt)) MARK(U52(s(z0), x1)) -> c66(A__U52(s(mark(z0)), x1), MARK(s(z0))) MARK(U52(nil, x1)) -> c66(A__U52(nil, x1), MARK(nil)) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1), MARK(zeros)) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(cons(z0, z1), x1)) -> c66(A__U52(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U52(0, x1)) -> c66(A__U52(0, x1), MARK(0)) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1), MARK(tt)) MARK(U52(s(z0), x1)) -> c66(A__U52(s(mark(z0)), x1), MARK(s(z0))) MARK(U52(nil, x1)) -> c66(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2 ---------------------------------------- (109) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(U52(nil, x1)) -> c66(A__U52(nil, x1), MARK(nil)) MARK(U52(0, x1)) -> c66(A__U52(0, x1), MARK(0)) ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1), MARK(zeros)) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(cons(z0, z1), x1)) -> c66(A__U52(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1), MARK(tt)) MARK(U52(s(z0), x1)) -> c66(A__U52(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1), MARK(zeros)) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(cons(z0, z1), x1)) -> c66(A__U52(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1), MARK(tt)) MARK(U52(s(z0), x1)) -> c66(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2 ---------------------------------------- (111) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c68_2, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1 ---------------------------------------- (113) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) by MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1), MARK(zeros)) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(cons(z0, z1), x1)) -> c68(A__U61(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U61(0, x1)) -> c68(A__U61(0, x1), MARK(0)) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1), MARK(tt)) MARK(U61(s(z0), x1)) -> c68(A__U61(s(mark(z0)), x1), MARK(s(z0))) MARK(U61(nil, x1)) -> c68(A__U61(nil, x1), MARK(nil)) ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1), MARK(zeros)) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(cons(z0, z1), x1)) -> c68(A__U61(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U61(0, x1)) -> c68(A__U61(0, x1), MARK(0)) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1), MARK(tt)) MARK(U61(s(z0), x1)) -> c68(A__U61(s(mark(z0)), x1), MARK(s(z0))) MARK(U61(nil, x1)) -> c68(A__U61(nil, x1), MARK(nil)) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1), MARK(zeros)) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(cons(z0, z1), x1)) -> c68(A__U61(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U61(0, x1)) -> c68(A__U61(0, x1), MARK(0)) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1), MARK(tt)) MARK(U61(s(z0), x1)) -> c68(A__U61(s(mark(z0)), x1), MARK(s(z0))) MARK(U61(nil, x1)) -> c68(A__U61(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2 ---------------------------------------- (115) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(U61(0, x1)) -> c68(A__U61(0, x1), MARK(0)) MARK(U61(nil, x1)) -> c68(A__U61(nil, x1), MARK(nil)) ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1), MARK(zeros)) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(cons(z0, z1), x1)) -> c68(A__U61(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1), MARK(tt)) MARK(U61(s(z0), x1)) -> c68(A__U61(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1), MARK(zeros)) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(cons(z0, z1), x1)) -> c68(A__U61(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1), MARK(tt)) MARK(U61(s(z0), x1)) -> c68(A__U61(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2 ---------------------------------------- (117) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) 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z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c69_2, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1 ---------------------------------------- (119) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) by MARK(length(zeros)) -> c69(A__LENGTH(a__zeros), MARK(zeros)) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(0)) -> c69(A__LENGTH(0), MARK(0)) MARK(length(tt)) -> c69(A__LENGTH(tt), MARK(tt)) MARK(length(s(z0))) -> c69(A__LENGTH(s(mark(z0))), MARK(s(z0))) MARK(length(nil)) -> c69(A__LENGTH(nil), MARK(nil)) ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros), MARK(zeros)) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(0)) -> c69(A__LENGTH(0), MARK(0)) MARK(length(tt)) -> c69(A__LENGTH(tt), MARK(tt)) MARK(length(s(z0))) -> c69(A__LENGTH(s(mark(z0))), MARK(s(z0))) MARK(length(nil)) -> c69(A__LENGTH(nil), MARK(nil)) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros), MARK(zeros)) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(0)) -> c69(A__LENGTH(0), MARK(0)) MARK(length(tt)) -> c69(A__LENGTH(tt), MARK(tt)) MARK(length(s(z0))) -> c69(A__LENGTH(s(mark(z0))), MARK(s(z0))) MARK(length(nil)) -> c69(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2 ---------------------------------------- (121) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(length(tt)) -> c69(A__LENGTH(tt), MARK(tt)) MARK(length(0)) -> c69(A__LENGTH(0), MARK(0)) MARK(length(nil)) -> c69(A__LENGTH(nil), 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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros), MARK(zeros)) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c69(A__LENGTH(s(mark(z0))), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros), MARK(zeros)) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c69(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2 ---------------------------------------- (123) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) 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z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c70_2, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1 ---------------------------------------- (125) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) by MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1), MARK(zeros)) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(cons(z0, z1), x1)) -> c70(A__AND(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(and(0, x1)) -> c70(A__AND(0, x1), MARK(0)) MARK(and(tt, x1)) -> c70(A__AND(tt, x1), MARK(tt)) MARK(and(s(z0), x1)) -> c70(A__AND(s(mark(z0)), x1), MARK(s(z0))) MARK(and(nil, x1)) -> c70(A__AND(nil, x1), MARK(nil)) ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1), MARK(zeros)) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(cons(z0, z1), x1)) -> c70(A__AND(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(and(0, x1)) -> c70(A__AND(0, x1), MARK(0)) MARK(and(tt, x1)) -> c70(A__AND(tt, x1), MARK(tt)) MARK(and(s(z0), x1)) -> c70(A__AND(s(mark(z0)), x1), MARK(s(z0))) MARK(and(nil, x1)) -> c70(A__AND(nil, x1), MARK(nil)) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), 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MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), 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MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, 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MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1), MARK(zeros)) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(cons(z0, z1), x1)) -> c70(A__AND(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(and(0, x1)) -> c70(A__AND(0, x1), MARK(0)) MARK(and(tt, x1)) -> c70(A__AND(tt, x1), MARK(tt)) MARK(and(s(z0), x1)) -> c70(A__AND(s(mark(z0)), x1), MARK(s(z0))) MARK(and(nil, x1)) -> c70(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1, c70_2 ---------------------------------------- (127) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(and(0, x1)) -> c70(A__AND(0, x1), MARK(0)) MARK(and(nil, x1)) -> c70(A__AND(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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1), MARK(zeros)) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(cons(z0, z1), x1)) -> c70(A__AND(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1), MARK(tt)) MARK(and(s(z0), x1)) -> c70(A__AND(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1), MARK(zeros)) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(cons(z0, z1), x1)) -> c70(A__AND(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1), MARK(tt)) MARK(and(s(z0), x1)) -> c70(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1, c70_2 ---------------------------------------- (129) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) 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c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(z0))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1 ---------------------------------------- (131) 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(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1 ---------------------------------------- (133) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1 ---------------------------------------- (135) 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))) ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> 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c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c14_2 ---------------------------------------- (137) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, 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MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) 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z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c14_2 ---------------------------------------- (139) 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(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c14_2 ---------------------------------------- (141) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), 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c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_1, c20_2, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c14_2 ---------------------------------------- (143) 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))) ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_1, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c14_2, c20_2 ---------------------------------------- (145) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_1, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c14_2, c20_2 ---------------------------------------- (147) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U61(tt, U11(z0, z1)) -> c26(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) by A__U61(tt, U11(x0, z1)) -> c26(A__LENGTH(U11(mark(x0), z1)), MARK(U11(x0, z1))) A__U61(tt, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1)), MARK(U11(0, x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1)), MARK(U11(nil, x1))) ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(x0, z1)) -> c26(A__LENGTH(U11(mark(x0), z1)), MARK(U11(x0, z1))) A__U61(tt, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1)), MARK(U11(0, x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1)), MARK(U11(nil, x1))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) 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c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(x0, z1)) -> c26(A__LENGTH(U11(mark(x0), z1)), MARK(U11(x0, z1))) A__U61(tt, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1)), MARK(U11(0, x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(nil, x1)) -> c26(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_1, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c14_2, c20_2 ---------------------------------------- (149) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) 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c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_1, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c14_2, c20_2 ---------------------------------------- (151) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U61(tt, U12(z0)) -> c26(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) by A__U61(tt, U12(x0)) -> c26(A__LENGTH(U12(mark(x0))), MARK(U12(x0))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> c26(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U61(tt, U12(U21(z0, z1))) -> c26(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U61(tt, U12(U22(z0))) -> c26(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U61(tt, U12(isNat(z0))) -> c26(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U61(tt, U12(U31(z0, z1))) -> c26(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U61(tt, U12(U32(z0))) -> c26(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U61(tt, U12(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U61(tt, U12(U42(z0, z1))) -> c26(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U61(tt, U12(U43(z0))) -> c26(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U61(tt, U12(isNatIList(z0))) -> c26(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U61(tt, U12(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U61(tt, U12(U52(z0, z1))) -> c26(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U61(tt, U12(U53(z0))) -> c26(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U61(tt, U12(U61(z0, z1))) -> c26(A__LENGTH(a__U12(a__U61(mark(z0), z1))), MARK(U12(U61(z0, z1)))) A__U61(tt, U12(length(z0))) -> c26(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U61(tt, U12(and(z0, z1))) -> c26(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U61(tt, U12(isNatIListKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U61(tt, U12(isNatKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U61(tt, U12(cons(z0, z1))) -> c26(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U61(tt, U12(0)) -> c26(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U61(tt, U12(tt)) -> c26(A__LENGTH(a__U12(tt)), MARK(U12(tt))) A__U61(tt, U12(s(z0))) -> c26(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U61(tt, U12(nil)) -> c26(A__LENGTH(a__U12(nil)), MARK(U12(nil))) A__U61(tt, U12(x0)) -> c26(MARK(U12(x0))) ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) A__U61(tt, U12(x0)) -> c26(A__LENGTH(U12(mark(x0))), MARK(U12(x0))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> c26(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U61(tt, U12(U21(z0, z1))) -> c26(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U61(tt, U12(U22(z0))) -> c26(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U61(tt, U12(isNat(z0))) -> c26(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U61(tt, U12(U31(z0, z1))) -> c26(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U61(tt, U12(U32(z0))) -> c26(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U61(tt, U12(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U61(tt, U12(U42(z0, z1))) -> c26(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U61(tt, U12(U43(z0))) -> c26(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U61(tt, U12(isNatIList(z0))) -> c26(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U61(tt, U12(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U61(tt, U12(U52(z0, z1))) -> c26(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U61(tt, U12(U53(z0))) -> c26(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U61(tt, U12(U61(z0, z1))) -> c26(A__LENGTH(a__U12(a__U61(mark(z0), z1))), MARK(U12(U61(z0, z1)))) A__U61(tt, U12(length(z0))) -> c26(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U61(tt, U12(and(z0, z1))) -> c26(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U61(tt, U12(isNatIListKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U61(tt, U12(isNatKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U61(tt, U12(cons(z0, z1))) -> c26(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U61(tt, U12(0)) -> c26(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U61(tt, U12(tt)) -> c26(A__LENGTH(a__U12(tt)), MARK(U12(tt))) A__U61(tt, U12(s(z0))) -> c26(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U61(tt, U12(nil)) -> c26(A__LENGTH(a__U12(nil)), MARK(U12(nil))) A__U61(tt, U12(x0)) -> c26(MARK(U12(x0))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) A__U61(tt, U12(x0)) -> c26(A__LENGTH(U12(mark(x0))), MARK(U12(x0))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> c26(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U61(tt, U12(U21(z0, z1))) -> c26(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U61(tt, U12(U22(z0))) -> c26(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U61(tt, U12(isNat(z0))) -> c26(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U61(tt, U12(U31(z0, z1))) -> c26(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U61(tt, U12(U32(z0))) -> c26(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U61(tt, U12(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U61(tt, U12(U42(z0, z1))) -> c26(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U61(tt, U12(U43(z0))) -> c26(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U61(tt, U12(isNatIList(z0))) -> c26(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U61(tt, U12(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U61(tt, U12(U52(z0, z1))) -> c26(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U61(tt, U12(U53(z0))) -> c26(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U61(tt, U12(U61(z0, z1))) -> c26(A__LENGTH(a__U12(a__U61(mark(z0), z1))), MARK(U12(U61(z0, z1)))) A__U61(tt, U12(length(z0))) -> c26(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U61(tt, U12(and(z0, z1))) -> c26(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U61(tt, U12(isNatIListKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U61(tt, U12(isNatKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U61(tt, U12(cons(z0, z1))) -> c26(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U61(tt, U12(0)) -> c26(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U61(tt, U12(tt)) -> c26(A__LENGTH(a__U12(tt)), MARK(U12(tt))) A__U61(tt, U12(s(z0))) -> c26(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U61(tt, U12(nil)) -> c26(A__LENGTH(a__U12(nil)), MARK(U12(nil))) A__U61(tt, U12(x0)) -> c26(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_1, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c14_2, c20_2 ---------------------------------------- (153) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> 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c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, 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c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, 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c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> c26(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U61(tt, U12(U21(z0, z1))) -> c26(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U61(tt, U12(U22(z0))) -> c26(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U61(tt, U12(isNat(z0))) -> c26(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U61(tt, U12(U31(z0, z1))) -> c26(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U61(tt, U12(U32(z0))) -> c26(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U61(tt, U12(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U61(tt, U12(U42(z0, z1))) -> c26(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U61(tt, U12(U43(z0))) -> c26(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U61(tt, U12(isNatIList(z0))) -> c26(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U61(tt, U12(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U61(tt, U12(U52(z0, z1))) -> c26(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U61(tt, U12(U53(z0))) -> c26(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U61(tt, U12(U61(z0, z1))) -> c26(A__LENGTH(a__U12(a__U61(mark(z0), z1))), MARK(U12(U61(z0, z1)))) A__U61(tt, U12(length(z0))) -> c26(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U61(tt, U12(and(z0, z1))) -> c26(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U61(tt, U12(isNatIListKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U61(tt, U12(isNatKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U61(tt, U12(cons(z0, z1))) -> c26(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U61(tt, U12(0)) -> c26(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U61(tt, U12(tt)) -> c26(A__LENGTH(a__U12(tt)), MARK(U12(tt))) A__U61(tt, U12(s(z0))) -> c26(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U61(tt, U12(nil)) -> c26(A__LENGTH(a__U12(nil)), MARK(U12(nil))) A__U61(tt, U12(x0)) -> c26(MARK(U12(x0))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) 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MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> c26(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U61(tt, U12(U21(z0, z1))) -> c26(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U61(tt, U12(U22(z0))) -> c26(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U61(tt, U12(isNat(z0))) -> c26(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U61(tt, U12(U31(z0, z1))) -> c26(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U61(tt, U12(U32(z0))) -> c26(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U61(tt, U12(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U61(tt, U12(U42(z0, z1))) -> c26(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U61(tt, U12(U43(z0))) -> c26(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U61(tt, U12(isNatIList(z0))) -> c26(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U61(tt, U12(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U61(tt, U12(U52(z0, z1))) -> c26(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U61(tt, U12(U53(z0))) -> c26(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U61(tt, U12(U61(z0, z1))) -> c26(A__LENGTH(a__U12(a__U61(mark(z0), z1))), MARK(U12(U61(z0, z1)))) A__U61(tt, U12(length(z0))) -> c26(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U61(tt, U12(and(z0, z1))) -> c26(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U61(tt, U12(isNatIListKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U61(tt, U12(isNatKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U61(tt, U12(cons(z0, z1))) -> c26(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U61(tt, U12(0)) -> c26(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U61(tt, U12(tt)) -> c26(A__LENGTH(a__U12(tt)), MARK(U12(tt))) A__U61(tt, U12(s(z0))) -> c26(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U61(tt, U12(nil)) -> c26(A__LENGTH(a__U12(nil)), MARK(U12(nil))) A__U61(tt, U12(x0)) -> c26(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_1, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c14_2, c20_2 ---------------------------------------- (155) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) by A__U61(tt, isNatList(nil)) -> c26(A__LENGTH(tt), MARK(isNatList(nil))) A__U61(tt, isNatList(cons(z0, z1))) -> c26(A__LENGTH(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(cons(z0, z1)))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(isNatList(z0)), MARK(isNatList(z0))) ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> c26(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U61(tt, U12(U21(z0, z1))) -> c26(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U61(tt, U12(U22(z0))) -> c26(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U61(tt, U12(isNat(z0))) -> c26(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U61(tt, U12(U31(z0, z1))) -> c26(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U61(tt, U12(U32(z0))) -> c26(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U61(tt, U12(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U61(tt, U12(U42(z0, z1))) -> c26(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U61(tt, U12(U43(z0))) -> c26(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U61(tt, U12(isNatIList(z0))) -> c26(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U61(tt, U12(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U61(tt, U12(U52(z0, z1))) -> c26(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U61(tt, U12(U53(z0))) -> c26(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U61(tt, U12(U61(z0, z1))) -> c26(A__LENGTH(a__U12(a__U61(mark(z0), z1))), MARK(U12(U61(z0, z1)))) A__U61(tt, U12(length(z0))) -> c26(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U61(tt, U12(and(z0, z1))) -> c26(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U61(tt, U12(isNatIListKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U61(tt, U12(isNatKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U61(tt, U12(cons(z0, z1))) -> c26(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U61(tt, U12(0)) -> c26(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U61(tt, U12(tt)) -> c26(A__LENGTH(a__U12(tt)), MARK(U12(tt))) A__U61(tt, U12(s(z0))) -> c26(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U61(tt, U12(nil)) -> c26(A__LENGTH(a__U12(nil)), MARK(U12(nil))) A__U61(tt, U12(x0)) -> c26(MARK(U12(x0))) A__U61(tt, isNatList(nil)) -> c26(A__LENGTH(tt), MARK(isNatList(nil))) A__U61(tt, isNatList(cons(z0, z1))) -> c26(A__LENGTH(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(cons(z0, z1)))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(isNatList(z0)), MARK(isNatList(z0))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> 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c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), 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MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> c26(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U61(tt, U12(U21(z0, z1))) -> c26(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U61(tt, U12(U22(z0))) -> c26(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U61(tt, U12(isNat(z0))) -> c26(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U61(tt, U12(U31(z0, z1))) -> c26(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U61(tt, U12(U32(z0))) -> c26(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U61(tt, U12(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U61(tt, U12(U42(z0, z1))) -> c26(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U61(tt, U12(U43(z0))) -> c26(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U61(tt, U12(isNatIList(z0))) -> c26(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U61(tt, U12(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U61(tt, U12(U52(z0, z1))) -> c26(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U61(tt, U12(U53(z0))) -> c26(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U61(tt, U12(U61(z0, z1))) -> c26(A__LENGTH(a__U12(a__U61(mark(z0), z1))), MARK(U12(U61(z0, z1)))) A__U61(tt, U12(length(z0))) -> c26(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U61(tt, U12(and(z0, z1))) -> c26(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U61(tt, U12(isNatIListKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U61(tt, U12(isNatKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U61(tt, U12(cons(z0, z1))) -> c26(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U61(tt, U12(0)) -> c26(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U61(tt, U12(tt)) -> c26(A__LENGTH(a__U12(tt)), MARK(U12(tt))) A__U61(tt, U12(s(z0))) -> c26(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U61(tt, U12(nil)) -> c26(A__LENGTH(a__U12(nil)), MARK(U12(nil))) A__U61(tt, U12(x0)) -> c26(MARK(U12(x0))) A__U61(tt, isNatList(nil)) -> c26(A__LENGTH(tt), MARK(isNatList(nil))) A__U61(tt, isNatList(cons(z0, z1))) -> c26(A__LENGTH(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(cons(z0, z1)))) A__U61(tt, isNatList(z0)) -> c26(A__LENGTH(isNatList(z0)), MARK(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_1, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c14_2, c20_2 ---------------------------------------- (157) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> 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c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> c26(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U61(tt, U12(U21(z0, z1))) -> c26(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U61(tt, U12(U22(z0))) -> c26(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U61(tt, U12(isNat(z0))) -> c26(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U61(tt, U12(U31(z0, z1))) -> c26(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U61(tt, U12(U32(z0))) -> c26(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U61(tt, U12(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U61(tt, U12(U42(z0, z1))) -> c26(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U61(tt, U12(U43(z0))) -> c26(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U61(tt, U12(isNatIList(z0))) -> c26(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U61(tt, U12(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U61(tt, U12(U52(z0, z1))) -> c26(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U61(tt, U12(U53(z0))) -> c26(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U61(tt, U12(U61(z0, z1))) -> c26(A__LENGTH(a__U12(a__U61(mark(z0), z1))), MARK(U12(U61(z0, z1)))) A__U61(tt, U12(length(z0))) -> c26(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U61(tt, U12(and(z0, z1))) -> c26(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U61(tt, U12(isNatIListKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U61(tt, U12(isNatKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U61(tt, U12(cons(z0, z1))) -> c26(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U61(tt, U12(0)) -> c26(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U61(tt, U12(tt)) -> c26(A__LENGTH(a__U12(tt)), MARK(U12(tt))) A__U61(tt, U12(s(z0))) -> c26(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U61(tt, U12(nil)) -> c26(A__LENGTH(a__U12(nil)), MARK(U12(nil))) A__U61(tt, U12(x0)) -> c26(MARK(U12(x0))) A__U61(tt, isNatList(cons(z0, z1))) -> c26(A__LENGTH(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(cons(z0, z1)))) A__U61(tt, isNatList(nil)) -> c26(MARK(isNatList(nil))) A__U61(tt, isNatList(z0)) -> c26(MARK(isNatList(z0))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, 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MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> c26(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U61(tt, U12(U21(z0, z1))) -> c26(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U61(tt, U12(U22(z0))) -> c26(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U61(tt, U12(isNat(z0))) -> c26(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U61(tt, U12(U31(z0, z1))) -> c26(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U61(tt, U12(U32(z0))) -> c26(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U61(tt, U12(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U61(tt, U12(U42(z0, z1))) -> c26(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U61(tt, U12(U43(z0))) -> c26(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U61(tt, U12(isNatIList(z0))) -> c26(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U61(tt, U12(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U61(tt, U12(U52(z0, z1))) -> c26(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U61(tt, U12(U53(z0))) -> c26(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U61(tt, U12(U61(z0, z1))) -> c26(A__LENGTH(a__U12(a__U61(mark(z0), z1))), MARK(U12(U61(z0, z1)))) A__U61(tt, U12(length(z0))) -> c26(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U61(tt, U12(and(z0, z1))) -> c26(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U61(tt, U12(isNatIListKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U61(tt, U12(isNatKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U61(tt, U12(cons(z0, z1))) -> c26(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U61(tt, U12(0)) -> c26(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U61(tt, U12(tt)) -> c26(A__LENGTH(a__U12(tt)), MARK(U12(tt))) A__U61(tt, U12(s(z0))) -> c26(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U61(tt, U12(nil)) -> c26(A__LENGTH(a__U12(nil)), MARK(U12(nil))) A__U61(tt, U12(x0)) -> c26(MARK(U12(x0))) A__U61(tt, isNatList(cons(z0, z1))) -> c26(A__LENGTH(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(cons(z0, z1)))) A__U61(tt, isNatList(nil)) -> c26(MARK(isNatList(nil))) A__U61(tt, isNatList(z0)) -> c26(MARK(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_1, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c14_2, c20_2 ---------------------------------------- (159) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U61(tt, U21(z0, z1)) -> c26(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) by A__U61(tt, U21(x0, z1)) -> c26(A__LENGTH(U21(mark(x0), z1)), MARK(U21(x0, z1))) A__U61(tt, U21(zeros, x1)) -> c26(A__LENGTH(a__U21(a__zeros, x1)), MARK(U21(zeros, x1))) A__U61(tt, U21(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1)), MARK(U21(U11(z0, z1), x1))) A__U61(tt, U21(U12(z0), x1)) -> c26(A__LENGTH(a__U21(a__U12(mark(z0)), x1)), MARK(U21(U12(z0), x1))) A__U61(tt, U21(isNatList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatList(z0), x1)), MARK(U21(isNatList(z0), x1))) A__U61(tt, U21(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U21(mark(z0), z1), x1)), MARK(U21(U21(z0, z1), x1))) A__U61(tt, U21(U22(z0), x1)) -> c26(A__LENGTH(a__U21(a__U22(mark(z0)), x1)), MARK(U21(U22(z0), x1))) A__U61(tt, U21(isNat(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNat(z0), x1)), MARK(U21(isNat(z0), x1))) A__U61(tt, U21(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U31(mark(z0), z1), x1)), MARK(U21(U31(z0, z1), x1))) A__U61(tt, U21(U32(z0), x1)) -> c26(A__LENGTH(a__U21(a__U32(mark(z0)), x1)), MARK(U21(U32(z0), x1))) A__U61(tt, U21(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(U21(U41(z0, z1, z2), x1))) A__U61(tt, U21(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U42(mark(z0), z1), x1)), MARK(U21(U42(z0, z1), x1))) A__U61(tt, U21(U43(z0), x1)) -> c26(A__LENGTH(a__U21(a__U43(mark(z0)), x1)), MARK(U21(U43(z0), x1))) A__U61(tt, U21(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIList(z0), x1)), MARK(U21(isNatIList(z0), x1))) A__U61(tt, U21(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U51(mark(z0), z1, z2), x1)), MARK(U21(U51(z0, z1, z2), x1))) A__U61(tt, U21(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U52(mark(z0), z1), x1)), MARK(U21(U52(z0, z1), x1))) A__U61(tt, U21(U53(z0), x1)) -> c26(A__LENGTH(a__U21(a__U53(mark(z0)), x1)), MARK(U21(U53(z0), x1))) A__U61(tt, U21(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U61(mark(z0), z1), x1)), MARK(U21(U61(z0, z1), x1))) A__U61(tt, U21(length(z0), x1)) -> c26(A__LENGTH(a__U21(a__length(mark(z0)), x1)), MARK(U21(length(z0), x1))) A__U61(tt, U21(and(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__and(mark(z0), z1), x1)), MARK(U21(and(z0, z1), x1))) A__U61(tt, U21(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIListKind(z0), x1)), MARK(U21(isNatIListKind(z0), x1))) A__U61(tt, U21(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), x1)), MARK(U21(isNatKind(z0), x1))) A__U61(tt, U21(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U21(cons(mark(z0), z1), x1)), MARK(U21(cons(z0, z1), x1))) A__U61(tt, U21(0, x1)) -> c26(A__LENGTH(a__U21(0, x1)), MARK(U21(0, x1))) A__U61(tt, U21(tt, x1)) -> c26(A__LENGTH(a__U21(tt, x1)), MARK(U21(tt, x1))) A__U61(tt, U21(s(z0), x1)) -> c26(A__LENGTH(a__U21(s(mark(z0)), x1)), MARK(U21(s(z0), x1))) A__U61(tt, U21(nil, x1)) -> c26(A__LENGTH(a__U21(nil, x1)), MARK(U21(nil, x1))) ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> c26(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U61(tt, U12(U21(z0, z1))) -> c26(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U61(tt, U12(U22(z0))) -> c26(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U61(tt, U12(isNat(z0))) -> c26(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U61(tt, U12(U31(z0, z1))) -> c26(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U61(tt, U12(U32(z0))) -> c26(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U61(tt, U12(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U61(tt, U12(U42(z0, z1))) -> c26(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U61(tt, U12(U43(z0))) -> c26(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U61(tt, U12(isNatIList(z0))) -> c26(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U61(tt, U12(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U61(tt, U12(U52(z0, z1))) -> c26(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U61(tt, U12(U53(z0))) -> c26(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U61(tt, U12(U61(z0, z1))) -> c26(A__LENGTH(a__U12(a__U61(mark(z0), z1))), MARK(U12(U61(z0, z1)))) A__U61(tt, U12(length(z0))) -> c26(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U61(tt, U12(and(z0, z1))) -> c26(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U61(tt, U12(isNatIListKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U61(tt, U12(isNatKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U61(tt, U12(cons(z0, z1))) -> c26(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U61(tt, U12(0)) -> c26(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U61(tt, U12(tt)) -> c26(A__LENGTH(a__U12(tt)), MARK(U12(tt))) A__U61(tt, U12(s(z0))) -> c26(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U61(tt, U12(nil)) -> c26(A__LENGTH(a__U12(nil)), MARK(U12(nil))) A__U61(tt, U12(x0)) -> c26(MARK(U12(x0))) A__U61(tt, isNatList(cons(z0, z1))) -> c26(A__LENGTH(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(cons(z0, z1)))) A__U61(tt, isNatList(nil)) -> c26(MARK(isNatList(nil))) A__U61(tt, isNatList(z0)) -> c26(MARK(isNatList(z0))) A__U61(tt, U21(x0, z1)) -> c26(A__LENGTH(U21(mark(x0), z1)), MARK(U21(x0, z1))) A__U61(tt, U21(zeros, x1)) -> c26(A__LENGTH(a__U21(a__zeros, x1)), MARK(U21(zeros, x1))) A__U61(tt, U21(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1)), MARK(U21(U11(z0, z1), x1))) A__U61(tt, U21(U12(z0), x1)) -> c26(A__LENGTH(a__U21(a__U12(mark(z0)), x1)), MARK(U21(U12(z0), x1))) A__U61(tt, U21(isNatList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatList(z0), x1)), MARK(U21(isNatList(z0), x1))) A__U61(tt, U21(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U21(mark(z0), z1), x1)), MARK(U21(U21(z0, z1), x1))) A__U61(tt, U21(U22(z0), x1)) -> c26(A__LENGTH(a__U21(a__U22(mark(z0)), x1)), MARK(U21(U22(z0), x1))) A__U61(tt, U21(isNat(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNat(z0), x1)), MARK(U21(isNat(z0), x1))) A__U61(tt, U21(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U31(mark(z0), z1), x1)), MARK(U21(U31(z0, z1), x1))) A__U61(tt, U21(U32(z0), x1)) -> c26(A__LENGTH(a__U21(a__U32(mark(z0)), x1)), MARK(U21(U32(z0), x1))) A__U61(tt, U21(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(U21(U41(z0, z1, z2), x1))) A__U61(tt, U21(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U42(mark(z0), z1), x1)), MARK(U21(U42(z0, z1), x1))) A__U61(tt, U21(U43(z0), x1)) -> c26(A__LENGTH(a__U21(a__U43(mark(z0)), x1)), MARK(U21(U43(z0), x1))) A__U61(tt, U21(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIList(z0), x1)), MARK(U21(isNatIList(z0), x1))) A__U61(tt, U21(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U51(mark(z0), z1, z2), x1)), MARK(U21(U51(z0, z1, z2), x1))) A__U61(tt, U21(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U52(mark(z0), z1), x1)), MARK(U21(U52(z0, z1), x1))) A__U61(tt, U21(U53(z0), x1)) -> c26(A__LENGTH(a__U21(a__U53(mark(z0)), x1)), MARK(U21(U53(z0), x1))) A__U61(tt, U21(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U61(mark(z0), z1), x1)), MARK(U21(U61(z0, z1), x1))) A__U61(tt, U21(length(z0), x1)) -> c26(A__LENGTH(a__U21(a__length(mark(z0)), x1)), MARK(U21(length(z0), x1))) A__U61(tt, U21(and(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__and(mark(z0), z1), x1)), MARK(U21(and(z0, z1), x1))) A__U61(tt, U21(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIListKind(z0), x1)), MARK(U21(isNatIListKind(z0), x1))) A__U61(tt, U21(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), x1)), MARK(U21(isNatKind(z0), x1))) A__U61(tt, U21(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U21(cons(mark(z0), z1), x1)), MARK(U21(cons(z0, z1), x1))) A__U61(tt, U21(0, x1)) -> c26(A__LENGTH(a__U21(0, x1)), MARK(U21(0, x1))) A__U61(tt, U21(tt, x1)) -> c26(A__LENGTH(a__U21(tt, x1)), MARK(U21(tt, x1))) A__U61(tt, U21(s(z0), x1)) -> c26(A__LENGTH(a__U21(s(mark(z0)), x1)), MARK(U21(s(z0), x1))) A__U61(tt, U21(nil, x1)) -> c26(A__LENGTH(a__U21(nil, x1)), MARK(U21(nil, x1))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, 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MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> c26(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U61(tt, U12(U21(z0, z1))) -> c26(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U61(tt, U12(U22(z0))) -> c26(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U61(tt, U12(isNat(z0))) -> c26(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U61(tt, U12(U31(z0, z1))) -> c26(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U61(tt, U12(U32(z0))) -> c26(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U61(tt, U12(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U61(tt, U12(U42(z0, z1))) -> c26(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U61(tt, U12(U43(z0))) -> c26(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U61(tt, U12(isNatIList(z0))) -> c26(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U61(tt, U12(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U61(tt, U12(U52(z0, z1))) -> c26(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U61(tt, U12(U53(z0))) -> c26(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U61(tt, U12(U61(z0, z1))) -> c26(A__LENGTH(a__U12(a__U61(mark(z0), z1))), MARK(U12(U61(z0, z1)))) A__U61(tt, U12(length(z0))) -> c26(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U61(tt, U12(and(z0, z1))) -> c26(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U61(tt, U12(isNatIListKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U61(tt, U12(isNatKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U61(tt, U12(cons(z0, z1))) -> c26(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U61(tt, U12(0)) -> c26(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U61(tt, U12(tt)) -> c26(A__LENGTH(a__U12(tt)), MARK(U12(tt))) A__U61(tt, U12(s(z0))) -> c26(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U61(tt, U12(nil)) -> c26(A__LENGTH(a__U12(nil)), MARK(U12(nil))) A__U61(tt, U12(x0)) -> c26(MARK(U12(x0))) A__U61(tt, isNatList(cons(z0, z1))) -> c26(A__LENGTH(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(cons(z0, z1)))) A__U61(tt, isNatList(nil)) -> c26(MARK(isNatList(nil))) A__U61(tt, isNatList(z0)) -> c26(MARK(isNatList(z0))) A__U61(tt, U21(x0, z1)) -> c26(A__LENGTH(U21(mark(x0), z1)), MARK(U21(x0, z1))) A__U61(tt, U21(zeros, x1)) -> c26(A__LENGTH(a__U21(a__zeros, x1)), MARK(U21(zeros, x1))) A__U61(tt, U21(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1)), MARK(U21(U11(z0, z1), x1))) A__U61(tt, U21(U12(z0), x1)) -> c26(A__LENGTH(a__U21(a__U12(mark(z0)), x1)), MARK(U21(U12(z0), x1))) A__U61(tt, U21(isNatList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatList(z0), x1)), MARK(U21(isNatList(z0), x1))) A__U61(tt, U21(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U21(mark(z0), z1), x1)), MARK(U21(U21(z0, z1), x1))) A__U61(tt, U21(U22(z0), x1)) -> c26(A__LENGTH(a__U21(a__U22(mark(z0)), x1)), MARK(U21(U22(z0), x1))) A__U61(tt, U21(isNat(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNat(z0), x1)), MARK(U21(isNat(z0), x1))) A__U61(tt, U21(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U31(mark(z0), z1), x1)), MARK(U21(U31(z0, z1), x1))) A__U61(tt, U21(U32(z0), x1)) -> c26(A__LENGTH(a__U21(a__U32(mark(z0)), x1)), MARK(U21(U32(z0), x1))) A__U61(tt, U21(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(U21(U41(z0, z1, z2), x1))) A__U61(tt, U21(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U42(mark(z0), z1), x1)), MARK(U21(U42(z0, z1), x1))) A__U61(tt, U21(U43(z0), x1)) -> c26(A__LENGTH(a__U21(a__U43(mark(z0)), x1)), MARK(U21(U43(z0), x1))) A__U61(tt, U21(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIList(z0), x1)), MARK(U21(isNatIList(z0), x1))) A__U61(tt, U21(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U51(mark(z0), z1, z2), x1)), MARK(U21(U51(z0, z1, z2), x1))) A__U61(tt, U21(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U52(mark(z0), z1), x1)), MARK(U21(U52(z0, z1), x1))) A__U61(tt, U21(U53(z0), x1)) -> c26(A__LENGTH(a__U21(a__U53(mark(z0)), x1)), MARK(U21(U53(z0), x1))) A__U61(tt, U21(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U61(mark(z0), z1), x1)), MARK(U21(U61(z0, z1), x1))) A__U61(tt, U21(length(z0), x1)) -> c26(A__LENGTH(a__U21(a__length(mark(z0)), x1)), MARK(U21(length(z0), x1))) A__U61(tt, U21(and(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__and(mark(z0), z1), x1)), MARK(U21(and(z0, z1), x1))) A__U61(tt, U21(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIListKind(z0), x1)), MARK(U21(isNatIListKind(z0), x1))) A__U61(tt, U21(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), x1)), MARK(U21(isNatKind(z0), x1))) A__U61(tt, U21(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U21(cons(mark(z0), z1), x1)), MARK(U21(cons(z0, z1), x1))) A__U61(tt, U21(0, x1)) -> c26(A__LENGTH(a__U21(0, x1)), MARK(U21(0, x1))) A__U61(tt, U21(tt, x1)) -> c26(A__LENGTH(a__U21(tt, x1)), MARK(U21(tt, x1))) A__U61(tt, U21(s(z0), x1)) -> c26(A__LENGTH(a__U21(s(mark(z0)), x1)), MARK(U21(s(z0), x1))) A__U61(tt, U21(nil, x1)) -> c26(A__LENGTH(a__U21(nil, x1)), MARK(U21(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_1, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c14_2, c20_2 ---------------------------------------- (161) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) 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MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> c26(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U61(tt, U12(U21(z0, z1))) -> c26(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U61(tt, U12(U22(z0))) -> c26(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U61(tt, U12(isNat(z0))) -> c26(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U61(tt, U12(U31(z0, z1))) -> c26(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U61(tt, U12(U32(z0))) -> c26(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U61(tt, U12(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U61(tt, U12(U42(z0, z1))) -> c26(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U61(tt, U12(U43(z0))) -> c26(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U61(tt, U12(isNatIList(z0))) -> c26(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U61(tt, U12(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U61(tt, U12(U52(z0, z1))) -> c26(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U61(tt, U12(U53(z0))) -> c26(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U61(tt, U12(U61(z0, z1))) -> c26(A__LENGTH(a__U12(a__U61(mark(z0), z1))), MARK(U12(U61(z0, z1)))) A__U61(tt, U12(length(z0))) -> c26(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U61(tt, U12(and(z0, z1))) -> c26(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U61(tt, U12(isNatIListKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U61(tt, U12(isNatKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U61(tt, U12(cons(z0, z1))) -> c26(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U61(tt, U12(0)) -> c26(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U61(tt, U12(tt)) -> c26(A__LENGTH(a__U12(tt)), MARK(U12(tt))) A__U61(tt, U12(s(z0))) -> c26(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U61(tt, U12(nil)) -> c26(A__LENGTH(a__U12(nil)), MARK(U12(nil))) A__U61(tt, U12(x0)) -> c26(MARK(U12(x0))) A__U61(tt, isNatList(cons(z0, z1))) -> c26(A__LENGTH(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(cons(z0, z1)))) A__U61(tt, isNatList(nil)) -> c26(MARK(isNatList(nil))) A__U61(tt, isNatList(z0)) -> c26(MARK(isNatList(z0))) A__U61(tt, U21(zeros, x1)) -> c26(A__LENGTH(a__U21(a__zeros, x1)), MARK(U21(zeros, x1))) A__U61(tt, U21(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1)), MARK(U21(U11(z0, z1), x1))) A__U61(tt, U21(U12(z0), x1)) -> c26(A__LENGTH(a__U21(a__U12(mark(z0)), x1)), MARK(U21(U12(z0), x1))) A__U61(tt, U21(isNatList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatList(z0), x1)), MARK(U21(isNatList(z0), x1))) A__U61(tt, U21(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U21(mark(z0), z1), x1)), MARK(U21(U21(z0, z1), x1))) A__U61(tt, U21(U22(z0), x1)) -> c26(A__LENGTH(a__U21(a__U22(mark(z0)), x1)), MARK(U21(U22(z0), x1))) A__U61(tt, U21(isNat(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNat(z0), x1)), MARK(U21(isNat(z0), x1))) A__U61(tt, U21(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U31(mark(z0), z1), x1)), MARK(U21(U31(z0, z1), x1))) A__U61(tt, U21(U32(z0), x1)) -> c26(A__LENGTH(a__U21(a__U32(mark(z0)), x1)), MARK(U21(U32(z0), x1))) A__U61(tt, U21(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(U21(U41(z0, z1, z2), x1))) A__U61(tt, U21(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U42(mark(z0), z1), x1)), MARK(U21(U42(z0, z1), x1))) A__U61(tt, U21(U43(z0), x1)) -> c26(A__LENGTH(a__U21(a__U43(mark(z0)), x1)), MARK(U21(U43(z0), x1))) A__U61(tt, U21(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIList(z0), x1)), MARK(U21(isNatIList(z0), x1))) A__U61(tt, U21(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U51(mark(z0), z1, z2), x1)), MARK(U21(U51(z0, z1, z2), x1))) A__U61(tt, U21(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U52(mark(z0), z1), x1)), MARK(U21(U52(z0, z1), x1))) A__U61(tt, U21(U53(z0), x1)) -> c26(A__LENGTH(a__U21(a__U53(mark(z0)), x1)), MARK(U21(U53(z0), x1))) A__U61(tt, U21(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U61(mark(z0), z1), x1)), MARK(U21(U61(z0, z1), x1))) A__U61(tt, U21(length(z0), x1)) -> c26(A__LENGTH(a__U21(a__length(mark(z0)), x1)), MARK(U21(length(z0), x1))) A__U61(tt, U21(and(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__and(mark(z0), z1), x1)), MARK(U21(and(z0, z1), x1))) A__U61(tt, U21(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIListKind(z0), x1)), MARK(U21(isNatIListKind(z0), x1))) A__U61(tt, U21(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), x1)), MARK(U21(isNatKind(z0), x1))) A__U61(tt, U21(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U21(cons(mark(z0), z1), x1)), MARK(U21(cons(z0, z1), x1))) A__U61(tt, U21(tt, x1)) -> c26(A__LENGTH(a__U21(tt, x1)), MARK(U21(tt, x1))) A__U61(tt, U21(s(z0), x1)) -> c26(A__LENGTH(a__U21(s(mark(z0)), x1)), MARK(U21(s(z0), x1))) A__U61(tt, U21(x0, z1)) -> c26(MARK(U21(x0, z1))) A__U61(tt, U21(0, x1)) -> c26(A__LENGTH(a__U21(0, x1))) A__U61(tt, U21(nil, x1)) -> c26(A__LENGTH(a__U21(nil, x1))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) 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A__U61(tt, U12(U43(z0))) -> c26(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U61(tt, U12(isNatIList(z0))) -> c26(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U61(tt, U12(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U61(tt, U12(U52(z0, z1))) -> c26(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U61(tt, U12(U53(z0))) -> c26(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U61(tt, U12(U61(z0, z1))) -> c26(A__LENGTH(a__U12(a__U61(mark(z0), z1))), MARK(U12(U61(z0, z1)))) A__U61(tt, U12(length(z0))) -> c26(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U61(tt, U12(and(z0, z1))) -> c26(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U61(tt, U12(isNatIListKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U61(tt, U12(isNatKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U61(tt, U12(cons(z0, z1))) -> c26(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U61(tt, U12(0)) -> c26(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U61(tt, U12(tt)) -> c26(A__LENGTH(a__U12(tt)), MARK(U12(tt))) A__U61(tt, U12(s(z0))) -> c26(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U61(tt, U12(nil)) -> c26(A__LENGTH(a__U12(nil)), MARK(U12(nil))) A__U61(tt, U12(x0)) -> c26(MARK(U12(x0))) A__U61(tt, isNatList(cons(z0, z1))) -> c26(A__LENGTH(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(cons(z0, z1)))) A__U61(tt, isNatList(nil)) -> c26(MARK(isNatList(nil))) A__U61(tt, isNatList(z0)) -> c26(MARK(isNatList(z0))) A__U61(tt, U21(zeros, x1)) -> c26(A__LENGTH(a__U21(a__zeros, x1)), MARK(U21(zeros, x1))) A__U61(tt, U21(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1)), MARK(U21(U11(z0, z1), x1))) A__U61(tt, U21(U12(z0), x1)) -> c26(A__LENGTH(a__U21(a__U12(mark(z0)), x1)), MARK(U21(U12(z0), x1))) A__U61(tt, U21(isNatList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatList(z0), x1)), MARK(U21(isNatList(z0), x1))) A__U61(tt, U21(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U21(mark(z0), z1), x1)), MARK(U21(U21(z0, z1), x1))) A__U61(tt, U21(U22(z0), x1)) -> c26(A__LENGTH(a__U21(a__U22(mark(z0)), x1)), MARK(U21(U22(z0), x1))) A__U61(tt, U21(isNat(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNat(z0), x1)), MARK(U21(isNat(z0), x1))) A__U61(tt, U21(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U31(mark(z0), z1), x1)), MARK(U21(U31(z0, z1), x1))) A__U61(tt, U21(U32(z0), x1)) -> c26(A__LENGTH(a__U21(a__U32(mark(z0)), x1)), MARK(U21(U32(z0), x1))) A__U61(tt, U21(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(U21(U41(z0, z1, z2), x1))) A__U61(tt, U21(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U42(mark(z0), z1), x1)), MARK(U21(U42(z0, z1), x1))) A__U61(tt, U21(U43(z0), x1)) -> c26(A__LENGTH(a__U21(a__U43(mark(z0)), x1)), MARK(U21(U43(z0), x1))) A__U61(tt, U21(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIList(z0), x1)), MARK(U21(isNatIList(z0), x1))) A__U61(tt, U21(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U51(mark(z0), z1, z2), x1)), MARK(U21(U51(z0, z1, z2), x1))) A__U61(tt, U21(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U52(mark(z0), z1), x1)), MARK(U21(U52(z0, z1), x1))) A__U61(tt, U21(U53(z0), x1)) -> c26(A__LENGTH(a__U21(a__U53(mark(z0)), x1)), MARK(U21(U53(z0), x1))) A__U61(tt, U21(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U61(mark(z0), z1), x1)), MARK(U21(U61(z0, z1), x1))) A__U61(tt, U21(length(z0), x1)) -> c26(A__LENGTH(a__U21(a__length(mark(z0)), x1)), MARK(U21(length(z0), x1))) A__U61(tt, U21(and(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__and(mark(z0), z1), x1)), MARK(U21(and(z0, z1), x1))) A__U61(tt, U21(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIListKind(z0), x1)), MARK(U21(isNatIListKind(z0), x1))) A__U61(tt, U21(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), x1)), MARK(U21(isNatKind(z0), x1))) A__U61(tt, U21(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U21(cons(mark(z0), z1), x1)), MARK(U21(cons(z0, z1), x1))) A__U61(tt, U21(tt, x1)) -> c26(A__LENGTH(a__U21(tt, x1)), MARK(U21(tt, x1))) A__U61(tt, U21(s(z0), x1)) -> c26(A__LENGTH(a__U21(s(mark(z0)), x1)), MARK(U21(s(z0), x1))) A__U61(tt, U21(x0, z1)) -> c26(MARK(U21(x0, z1))) A__U61(tt, U21(0, x1)) -> c26(A__LENGTH(a__U21(0, x1))) A__U61(tt, U21(nil, x1)) -> c26(A__LENGTH(a__U21(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_1, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c14_2, c20_2 ---------------------------------------- (163) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U61(tt, U22(z0)) -> c26(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) by A__U61(tt, U22(x0)) -> c26(A__LENGTH(U22(mark(x0))), MARK(U22(x0))) A__U61(tt, U22(zeros)) -> c26(A__LENGTH(a__U22(a__zeros)), MARK(U22(zeros))) A__U61(tt, U22(U11(z0, z1))) -> c26(A__LENGTH(a__U22(a__U11(mark(z0), z1))), MARK(U22(U11(z0, z1)))) A__U61(tt, U22(U12(z0))) -> c26(A__LENGTH(a__U22(a__U12(mark(z0)))), MARK(U22(U12(z0)))) A__U61(tt, U22(isNatList(z0))) -> c26(A__LENGTH(a__U22(a__isNatList(z0))), MARK(U22(isNatList(z0)))) A__U61(tt, U22(U21(z0, z1))) -> c26(A__LENGTH(a__U22(a__U21(mark(z0), z1))), MARK(U22(U21(z0, z1)))) A__U61(tt, U22(U22(z0))) -> c26(A__LENGTH(a__U22(a__U22(mark(z0)))), MARK(U22(U22(z0)))) A__U61(tt, U22(isNat(z0))) -> c26(A__LENGTH(a__U22(a__isNat(z0))), MARK(U22(isNat(z0)))) A__U61(tt, U22(U31(z0, z1))) -> c26(A__LENGTH(a__U22(a__U31(mark(z0), z1))), MARK(U22(U31(z0, z1)))) A__U61(tt, U22(U32(z0))) -> c26(A__LENGTH(a__U22(a__U32(mark(z0)))), MARK(U22(U32(z0)))) A__U61(tt, U22(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U22(a__U41(mark(z0), z1, z2))), MARK(U22(U41(z0, z1, z2)))) A__U61(tt, U22(U42(z0, z1))) -> c26(A__LENGTH(a__U22(a__U42(mark(z0), z1))), MARK(U22(U42(z0, z1)))) A__U61(tt, U22(U43(z0))) -> c26(A__LENGTH(a__U22(a__U43(mark(z0)))), MARK(U22(U43(z0)))) A__U61(tt, U22(isNatIList(z0))) -> c26(A__LENGTH(a__U22(a__isNatIList(z0))), MARK(U22(isNatIList(z0)))) A__U61(tt, U22(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U22(a__U51(mark(z0), z1, z2))), MARK(U22(U51(z0, z1, z2)))) A__U61(tt, U22(U52(z0, z1))) -> c26(A__LENGTH(a__U22(a__U52(mark(z0), z1))), MARK(U22(U52(z0, z1)))) A__U61(tt, U22(U53(z0))) -> c26(A__LENGTH(a__U22(a__U53(mark(z0)))), MARK(U22(U53(z0)))) A__U61(tt, U22(U61(z0, z1))) -> c26(A__LENGTH(a__U22(a__U61(mark(z0), z1))), MARK(U22(U61(z0, z1)))) A__U61(tt, U22(length(z0))) -> c26(A__LENGTH(a__U22(a__length(mark(z0)))), MARK(U22(length(z0)))) A__U61(tt, U22(and(z0, z1))) -> c26(A__LENGTH(a__U22(a__and(mark(z0), z1))), MARK(U22(and(z0, z1)))) A__U61(tt, U22(isNatIListKind(z0))) -> c26(A__LENGTH(a__U22(a__isNatIListKind(z0))), MARK(U22(isNatIListKind(z0)))) A__U61(tt, U22(isNatKind(z0))) -> c26(A__LENGTH(a__U22(a__isNatKind(z0))), MARK(U22(isNatKind(z0)))) A__U61(tt, U22(cons(z0, z1))) -> c26(A__LENGTH(a__U22(cons(mark(z0), z1))), MARK(U22(cons(z0, z1)))) A__U61(tt, U22(0)) -> c26(A__LENGTH(a__U22(0)), MARK(U22(0))) A__U61(tt, U22(tt)) -> c26(A__LENGTH(a__U22(tt)), MARK(U22(tt))) A__U61(tt, U22(s(z0))) -> c26(A__LENGTH(a__U22(s(mark(z0)))), MARK(U22(s(z0)))) A__U61(tt, U22(nil)) -> c26(A__LENGTH(a__U22(nil)), MARK(U22(nil))) A__U61(tt, U22(x0)) -> c26(MARK(U22(x0))) ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> 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c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), 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MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> c26(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U61(tt, U12(U21(z0, z1))) -> c26(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U61(tt, U12(U22(z0))) -> c26(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U61(tt, U12(isNat(z0))) -> c26(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U61(tt, U12(U31(z0, z1))) -> c26(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U61(tt, U12(U32(z0))) -> c26(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U61(tt, U12(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U61(tt, U12(U42(z0, z1))) -> c26(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U61(tt, U12(U43(z0))) -> c26(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U61(tt, U12(isNatIList(z0))) -> c26(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U61(tt, U12(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U61(tt, U12(U52(z0, z1))) -> c26(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U61(tt, U12(U53(z0))) -> c26(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U61(tt, U12(U61(z0, z1))) -> c26(A__LENGTH(a__U12(a__U61(mark(z0), z1))), MARK(U12(U61(z0, z1)))) A__U61(tt, U12(length(z0))) -> c26(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U61(tt, U12(and(z0, z1))) -> c26(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U61(tt, U12(isNatIListKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U61(tt, U12(isNatKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U61(tt, U12(cons(z0, z1))) -> c26(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U61(tt, U12(0)) -> c26(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U61(tt, U12(tt)) -> c26(A__LENGTH(a__U12(tt)), MARK(U12(tt))) A__U61(tt, U12(s(z0))) -> c26(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U61(tt, U12(nil)) -> c26(A__LENGTH(a__U12(nil)), MARK(U12(nil))) A__U61(tt, U12(x0)) -> c26(MARK(U12(x0))) A__U61(tt, isNatList(cons(z0, z1))) -> c26(A__LENGTH(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(cons(z0, z1)))) A__U61(tt, isNatList(nil)) -> c26(MARK(isNatList(nil))) A__U61(tt, isNatList(z0)) -> c26(MARK(isNatList(z0))) A__U61(tt, U21(zeros, x1)) -> c26(A__LENGTH(a__U21(a__zeros, x1)), MARK(U21(zeros, x1))) A__U61(tt, U21(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1)), MARK(U21(U11(z0, z1), x1))) A__U61(tt, U21(U12(z0), x1)) -> c26(A__LENGTH(a__U21(a__U12(mark(z0)), x1)), MARK(U21(U12(z0), x1))) A__U61(tt, U21(isNatList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatList(z0), x1)), MARK(U21(isNatList(z0), x1))) A__U61(tt, U21(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U21(mark(z0), z1), x1)), MARK(U21(U21(z0, z1), x1))) A__U61(tt, U21(U22(z0), x1)) -> c26(A__LENGTH(a__U21(a__U22(mark(z0)), x1)), MARK(U21(U22(z0), x1))) A__U61(tt, U21(isNat(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNat(z0), x1)), MARK(U21(isNat(z0), x1))) A__U61(tt, U21(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U31(mark(z0), z1), x1)), MARK(U21(U31(z0, z1), x1))) A__U61(tt, U21(U32(z0), x1)) -> c26(A__LENGTH(a__U21(a__U32(mark(z0)), x1)), MARK(U21(U32(z0), x1))) A__U61(tt, U21(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(U21(U41(z0, z1, z2), x1))) A__U61(tt, U21(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U42(mark(z0), z1), x1)), MARK(U21(U42(z0, z1), x1))) A__U61(tt, U21(U43(z0), x1)) -> c26(A__LENGTH(a__U21(a__U43(mark(z0)), x1)), MARK(U21(U43(z0), x1))) A__U61(tt, U21(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIList(z0), x1)), MARK(U21(isNatIList(z0), x1))) A__U61(tt, U21(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U51(mark(z0), z1, z2), x1)), MARK(U21(U51(z0, z1, z2), x1))) A__U61(tt, U21(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U52(mark(z0), z1), x1)), MARK(U21(U52(z0, z1), x1))) A__U61(tt, U21(U53(z0), x1)) -> c26(A__LENGTH(a__U21(a__U53(mark(z0)), x1)), MARK(U21(U53(z0), x1))) A__U61(tt, U21(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U61(mark(z0), z1), x1)), MARK(U21(U61(z0, z1), x1))) A__U61(tt, U21(length(z0), x1)) -> c26(A__LENGTH(a__U21(a__length(mark(z0)), x1)), MARK(U21(length(z0), x1))) A__U61(tt, U21(and(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__and(mark(z0), z1), x1)), MARK(U21(and(z0, z1), x1))) A__U61(tt, U21(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIListKind(z0), x1)), MARK(U21(isNatIListKind(z0), x1))) A__U61(tt, U21(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), x1)), MARK(U21(isNatKind(z0), x1))) A__U61(tt, U21(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U21(cons(mark(z0), z1), x1)), MARK(U21(cons(z0, z1), x1))) A__U61(tt, U21(tt, x1)) -> c26(A__LENGTH(a__U21(tt, x1)), MARK(U21(tt, x1))) A__U61(tt, U21(s(z0), x1)) -> c26(A__LENGTH(a__U21(s(mark(z0)), x1)), MARK(U21(s(z0), x1))) A__U61(tt, U21(x0, z1)) -> c26(MARK(U21(x0, z1))) A__U61(tt, U21(0, x1)) -> c26(A__LENGTH(a__U21(0, x1))) A__U61(tt, U21(nil, x1)) -> c26(A__LENGTH(a__U21(nil, x1))) A__U61(tt, U22(x0)) -> c26(A__LENGTH(U22(mark(x0))), MARK(U22(x0))) A__U61(tt, U22(zeros)) -> c26(A__LENGTH(a__U22(a__zeros)), MARK(U22(zeros))) A__U61(tt, U22(U11(z0, z1))) -> c26(A__LENGTH(a__U22(a__U11(mark(z0), z1))), MARK(U22(U11(z0, z1)))) A__U61(tt, U22(U12(z0))) -> c26(A__LENGTH(a__U22(a__U12(mark(z0)))), MARK(U22(U12(z0)))) A__U61(tt, U22(isNatList(z0))) -> c26(A__LENGTH(a__U22(a__isNatList(z0))), MARK(U22(isNatList(z0)))) A__U61(tt, U22(U21(z0, z1))) -> c26(A__LENGTH(a__U22(a__U21(mark(z0), z1))), MARK(U22(U21(z0, z1)))) A__U61(tt, U22(U22(z0))) -> c26(A__LENGTH(a__U22(a__U22(mark(z0)))), MARK(U22(U22(z0)))) A__U61(tt, U22(isNat(z0))) -> c26(A__LENGTH(a__U22(a__isNat(z0))), MARK(U22(isNat(z0)))) A__U61(tt, U22(U31(z0, z1))) -> c26(A__LENGTH(a__U22(a__U31(mark(z0), z1))), MARK(U22(U31(z0, z1)))) A__U61(tt, U22(U32(z0))) -> c26(A__LENGTH(a__U22(a__U32(mark(z0)))), MARK(U22(U32(z0)))) A__U61(tt, U22(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U22(a__U41(mark(z0), z1, z2))), MARK(U22(U41(z0, z1, z2)))) A__U61(tt, U22(U42(z0, z1))) -> c26(A__LENGTH(a__U22(a__U42(mark(z0), z1))), MARK(U22(U42(z0, z1)))) A__U61(tt, U22(U43(z0))) -> c26(A__LENGTH(a__U22(a__U43(mark(z0)))), MARK(U22(U43(z0)))) A__U61(tt, U22(isNatIList(z0))) -> c26(A__LENGTH(a__U22(a__isNatIList(z0))), MARK(U22(isNatIList(z0)))) A__U61(tt, U22(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U22(a__U51(mark(z0), z1, z2))), MARK(U22(U51(z0, z1, z2)))) A__U61(tt, U22(U52(z0, z1))) -> c26(A__LENGTH(a__U22(a__U52(mark(z0), z1))), MARK(U22(U52(z0, z1)))) A__U61(tt, U22(U53(z0))) -> c26(A__LENGTH(a__U22(a__U53(mark(z0)))), MARK(U22(U53(z0)))) A__U61(tt, U22(U61(z0, z1))) -> c26(A__LENGTH(a__U22(a__U61(mark(z0), z1))), MARK(U22(U61(z0, z1)))) A__U61(tt, U22(length(z0))) -> c26(A__LENGTH(a__U22(a__length(mark(z0)))), MARK(U22(length(z0)))) A__U61(tt, U22(and(z0, z1))) -> c26(A__LENGTH(a__U22(a__and(mark(z0), z1))), MARK(U22(and(z0, z1)))) A__U61(tt, U22(isNatIListKind(z0))) -> c26(A__LENGTH(a__U22(a__isNatIListKind(z0))), MARK(U22(isNatIListKind(z0)))) A__U61(tt, U22(isNatKind(z0))) -> c26(A__LENGTH(a__U22(a__isNatKind(z0))), MARK(U22(isNatKind(z0)))) A__U61(tt, U22(cons(z0, z1))) -> c26(A__LENGTH(a__U22(cons(mark(z0), z1))), MARK(U22(cons(z0, z1)))) A__U61(tt, U22(0)) -> c26(A__LENGTH(a__U22(0)), MARK(U22(0))) A__U61(tt, U22(tt)) -> c26(A__LENGTH(a__U22(tt)), MARK(U22(tt))) A__U61(tt, U22(s(z0))) -> c26(A__LENGTH(a__U22(s(mark(z0)))), MARK(U22(s(z0)))) A__U61(tt, U22(nil)) -> c26(A__LENGTH(a__U22(nil)), MARK(U22(nil))) A__U61(tt, U22(x0)) -> c26(MARK(U22(x0))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), 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MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> c26(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U61(tt, U12(U21(z0, z1))) -> c26(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U61(tt, U12(U22(z0))) -> c26(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U61(tt, U12(isNat(z0))) -> c26(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U61(tt, U12(U31(z0, z1))) -> c26(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U61(tt, U12(U32(z0))) -> c26(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U61(tt, U12(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U61(tt, U12(U42(z0, z1))) -> c26(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U61(tt, U12(U43(z0))) -> c26(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U61(tt, U12(isNatIList(z0))) -> c26(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U61(tt, U12(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U61(tt, U12(U52(z0, z1))) -> c26(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U61(tt, U12(U53(z0))) -> c26(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U61(tt, U12(U61(z0, z1))) -> c26(A__LENGTH(a__U12(a__U61(mark(z0), z1))), MARK(U12(U61(z0, z1)))) A__U61(tt, U12(length(z0))) -> c26(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U61(tt, U12(and(z0, z1))) -> c26(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U61(tt, U12(isNatIListKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U61(tt, U12(isNatKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U61(tt, U12(cons(z0, z1))) -> c26(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U61(tt, U12(0)) -> c26(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U61(tt, U12(tt)) -> c26(A__LENGTH(a__U12(tt)), MARK(U12(tt))) A__U61(tt, U12(s(z0))) -> c26(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U61(tt, U12(nil)) -> c26(A__LENGTH(a__U12(nil)), MARK(U12(nil))) A__U61(tt, U12(x0)) -> c26(MARK(U12(x0))) A__U61(tt, isNatList(cons(z0, z1))) -> c26(A__LENGTH(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(cons(z0, z1)))) A__U61(tt, isNatList(nil)) -> c26(MARK(isNatList(nil))) A__U61(tt, isNatList(z0)) -> c26(MARK(isNatList(z0))) A__U61(tt, U21(zeros, x1)) -> c26(A__LENGTH(a__U21(a__zeros, x1)), MARK(U21(zeros, x1))) A__U61(tt, U21(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1)), MARK(U21(U11(z0, z1), x1))) A__U61(tt, U21(U12(z0), x1)) -> c26(A__LENGTH(a__U21(a__U12(mark(z0)), x1)), MARK(U21(U12(z0), x1))) A__U61(tt, U21(isNatList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatList(z0), x1)), MARK(U21(isNatList(z0), x1))) A__U61(tt, U21(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U21(mark(z0), z1), x1)), MARK(U21(U21(z0, z1), x1))) A__U61(tt, U21(U22(z0), x1)) -> c26(A__LENGTH(a__U21(a__U22(mark(z0)), x1)), MARK(U21(U22(z0), x1))) A__U61(tt, U21(isNat(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNat(z0), x1)), MARK(U21(isNat(z0), x1))) A__U61(tt, U21(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U31(mark(z0), z1), x1)), MARK(U21(U31(z0, z1), x1))) A__U61(tt, U21(U32(z0), x1)) -> c26(A__LENGTH(a__U21(a__U32(mark(z0)), x1)), MARK(U21(U32(z0), x1))) A__U61(tt, U21(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(U21(U41(z0, z1, z2), x1))) A__U61(tt, U21(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U42(mark(z0), z1), x1)), MARK(U21(U42(z0, z1), x1))) A__U61(tt, U21(U43(z0), x1)) -> c26(A__LENGTH(a__U21(a__U43(mark(z0)), x1)), MARK(U21(U43(z0), x1))) A__U61(tt, U21(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIList(z0), x1)), MARK(U21(isNatIList(z0), x1))) A__U61(tt, U21(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U51(mark(z0), z1, z2), x1)), MARK(U21(U51(z0, z1, z2), x1))) A__U61(tt, U21(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U52(mark(z0), z1), x1)), MARK(U21(U52(z0, z1), x1))) A__U61(tt, U21(U53(z0), x1)) -> c26(A__LENGTH(a__U21(a__U53(mark(z0)), x1)), MARK(U21(U53(z0), x1))) A__U61(tt, U21(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U61(mark(z0), z1), x1)), MARK(U21(U61(z0, z1), x1))) A__U61(tt, U21(length(z0), x1)) -> c26(A__LENGTH(a__U21(a__length(mark(z0)), x1)), MARK(U21(length(z0), x1))) A__U61(tt, U21(and(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__and(mark(z0), z1), x1)), MARK(U21(and(z0, z1), x1))) A__U61(tt, U21(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIListKind(z0), x1)), MARK(U21(isNatIListKind(z0), x1))) A__U61(tt, U21(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), x1)), MARK(U21(isNatKind(z0), x1))) A__U61(tt, U21(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U21(cons(mark(z0), z1), x1)), MARK(U21(cons(z0, z1), x1))) A__U61(tt, U21(tt, x1)) -> c26(A__LENGTH(a__U21(tt, x1)), MARK(U21(tt, x1))) A__U61(tt, U21(s(z0), x1)) -> c26(A__LENGTH(a__U21(s(mark(z0)), x1)), MARK(U21(s(z0), x1))) A__U61(tt, U21(x0, z1)) -> c26(MARK(U21(x0, z1))) A__U61(tt, U21(0, x1)) -> c26(A__LENGTH(a__U21(0, x1))) A__U61(tt, U21(nil, x1)) -> c26(A__LENGTH(a__U21(nil, x1))) A__U61(tt, U22(x0)) -> c26(A__LENGTH(U22(mark(x0))), MARK(U22(x0))) A__U61(tt, U22(zeros)) -> c26(A__LENGTH(a__U22(a__zeros)), MARK(U22(zeros))) A__U61(tt, U22(U11(z0, z1))) -> c26(A__LENGTH(a__U22(a__U11(mark(z0), z1))), MARK(U22(U11(z0, z1)))) A__U61(tt, U22(U12(z0))) -> c26(A__LENGTH(a__U22(a__U12(mark(z0)))), MARK(U22(U12(z0)))) A__U61(tt, U22(isNatList(z0))) -> c26(A__LENGTH(a__U22(a__isNatList(z0))), MARK(U22(isNatList(z0)))) A__U61(tt, U22(U21(z0, z1))) -> c26(A__LENGTH(a__U22(a__U21(mark(z0), z1))), MARK(U22(U21(z0, z1)))) A__U61(tt, U22(U22(z0))) -> c26(A__LENGTH(a__U22(a__U22(mark(z0)))), MARK(U22(U22(z0)))) A__U61(tt, U22(isNat(z0))) -> c26(A__LENGTH(a__U22(a__isNat(z0))), MARK(U22(isNat(z0)))) A__U61(tt, U22(U31(z0, z1))) -> c26(A__LENGTH(a__U22(a__U31(mark(z0), z1))), MARK(U22(U31(z0, z1)))) A__U61(tt, U22(U32(z0))) -> c26(A__LENGTH(a__U22(a__U32(mark(z0)))), MARK(U22(U32(z0)))) A__U61(tt, U22(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U22(a__U41(mark(z0), z1, z2))), MARK(U22(U41(z0, z1, z2)))) A__U61(tt, U22(U42(z0, z1))) -> c26(A__LENGTH(a__U22(a__U42(mark(z0), z1))), MARK(U22(U42(z0, z1)))) A__U61(tt, U22(U43(z0))) -> c26(A__LENGTH(a__U22(a__U43(mark(z0)))), MARK(U22(U43(z0)))) A__U61(tt, U22(isNatIList(z0))) -> c26(A__LENGTH(a__U22(a__isNatIList(z0))), MARK(U22(isNatIList(z0)))) A__U61(tt, U22(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U22(a__U51(mark(z0), z1, z2))), MARK(U22(U51(z0, z1, z2)))) A__U61(tt, U22(U52(z0, z1))) -> c26(A__LENGTH(a__U22(a__U52(mark(z0), z1))), MARK(U22(U52(z0, z1)))) A__U61(tt, U22(U53(z0))) -> c26(A__LENGTH(a__U22(a__U53(mark(z0)))), MARK(U22(U53(z0)))) A__U61(tt, U22(U61(z0, z1))) -> c26(A__LENGTH(a__U22(a__U61(mark(z0), z1))), MARK(U22(U61(z0, z1)))) A__U61(tt, U22(length(z0))) -> c26(A__LENGTH(a__U22(a__length(mark(z0)))), MARK(U22(length(z0)))) A__U61(tt, U22(and(z0, z1))) -> c26(A__LENGTH(a__U22(a__and(mark(z0), z1))), MARK(U22(and(z0, z1)))) A__U61(tt, U22(isNatIListKind(z0))) -> c26(A__LENGTH(a__U22(a__isNatIListKind(z0))), MARK(U22(isNatIListKind(z0)))) A__U61(tt, U22(isNatKind(z0))) -> c26(A__LENGTH(a__U22(a__isNatKind(z0))), MARK(U22(isNatKind(z0)))) A__U61(tt, U22(cons(z0, z1))) -> c26(A__LENGTH(a__U22(cons(mark(z0), z1))), MARK(U22(cons(z0, z1)))) A__U61(tt, U22(0)) -> c26(A__LENGTH(a__U22(0)), MARK(U22(0))) A__U61(tt, U22(tt)) -> c26(A__LENGTH(a__U22(tt)), MARK(U22(tt))) A__U61(tt, U22(s(z0))) -> c26(A__LENGTH(a__U22(s(mark(z0)))), MARK(U22(s(z0)))) A__U61(tt, U22(nil)) -> c26(A__LENGTH(a__U22(nil)), MARK(U22(nil))) A__U61(tt, U22(x0)) -> c26(MARK(U22(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_1, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c14_2, c20_2 ---------------------------------------- (165) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> c26(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U61(tt, U12(U21(z0, z1))) -> c26(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U61(tt, U12(U22(z0))) -> c26(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U61(tt, U12(isNat(z0))) -> c26(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U61(tt, U12(U31(z0, z1))) -> c26(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U61(tt, U12(U32(z0))) -> c26(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U61(tt, U12(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U61(tt, U12(U42(z0, z1))) -> c26(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U61(tt, U12(U43(z0))) -> c26(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U61(tt, U12(isNatIList(z0))) -> c26(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U61(tt, U12(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U61(tt, U12(U52(z0, z1))) -> c26(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U61(tt, U12(U53(z0))) -> c26(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U61(tt, U12(U61(z0, z1))) -> c26(A__LENGTH(a__U12(a__U61(mark(z0), z1))), MARK(U12(U61(z0, z1)))) A__U61(tt, U12(length(z0))) -> c26(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U61(tt, U12(and(z0, z1))) -> c26(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U61(tt, U12(isNatIListKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U61(tt, U12(isNatKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U61(tt, U12(cons(z0, z1))) -> c26(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U61(tt, U12(0)) -> c26(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U61(tt, U12(tt)) -> c26(A__LENGTH(a__U12(tt)), MARK(U12(tt))) A__U61(tt, U12(s(z0))) -> c26(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U61(tt, U12(nil)) -> c26(A__LENGTH(a__U12(nil)), MARK(U12(nil))) A__U61(tt, U12(x0)) -> c26(MARK(U12(x0))) A__U61(tt, isNatList(cons(z0, z1))) -> c26(A__LENGTH(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(cons(z0, z1)))) A__U61(tt, isNatList(nil)) -> c26(MARK(isNatList(nil))) A__U61(tt, isNatList(z0)) -> c26(MARK(isNatList(z0))) A__U61(tt, U21(zeros, x1)) -> c26(A__LENGTH(a__U21(a__zeros, x1)), MARK(U21(zeros, x1))) A__U61(tt, U21(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1)), MARK(U21(U11(z0, z1), x1))) A__U61(tt, U21(U12(z0), x1)) -> c26(A__LENGTH(a__U21(a__U12(mark(z0)), x1)), MARK(U21(U12(z0), x1))) A__U61(tt, U21(isNatList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatList(z0), x1)), MARK(U21(isNatList(z0), x1))) A__U61(tt, U21(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U21(mark(z0), z1), x1)), MARK(U21(U21(z0, z1), x1))) A__U61(tt, U21(U22(z0), x1)) -> c26(A__LENGTH(a__U21(a__U22(mark(z0)), x1)), MARK(U21(U22(z0), x1))) A__U61(tt, U21(isNat(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNat(z0), x1)), MARK(U21(isNat(z0), x1))) A__U61(tt, U21(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U31(mark(z0), z1), x1)), MARK(U21(U31(z0, z1), x1))) A__U61(tt, U21(U32(z0), x1)) -> c26(A__LENGTH(a__U21(a__U32(mark(z0)), x1)), MARK(U21(U32(z0), x1))) A__U61(tt, U21(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(U21(U41(z0, z1, z2), x1))) A__U61(tt, U21(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U42(mark(z0), z1), x1)), MARK(U21(U42(z0, z1), x1))) A__U61(tt, U21(U43(z0), x1)) -> c26(A__LENGTH(a__U21(a__U43(mark(z0)), x1)), MARK(U21(U43(z0), x1))) A__U61(tt, U21(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIList(z0), x1)), MARK(U21(isNatIList(z0), x1))) A__U61(tt, U21(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U51(mark(z0), z1, z2), x1)), MARK(U21(U51(z0, z1, z2), x1))) A__U61(tt, U21(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U52(mark(z0), z1), x1)), MARK(U21(U52(z0, z1), x1))) A__U61(tt, U21(U53(z0), x1)) -> c26(A__LENGTH(a__U21(a__U53(mark(z0)), x1)), MARK(U21(U53(z0), x1))) A__U61(tt, U21(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U61(mark(z0), z1), x1)), MARK(U21(U61(z0, z1), x1))) A__U61(tt, U21(length(z0), x1)) -> c26(A__LENGTH(a__U21(a__length(mark(z0)), x1)), MARK(U21(length(z0), x1))) A__U61(tt, U21(and(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__and(mark(z0), z1), x1)), MARK(U21(and(z0, z1), x1))) A__U61(tt, U21(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIListKind(z0), x1)), MARK(U21(isNatIListKind(z0), x1))) A__U61(tt, U21(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), x1)), MARK(U21(isNatKind(z0), x1))) A__U61(tt, U21(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U21(cons(mark(z0), z1), x1)), MARK(U21(cons(z0, z1), x1))) A__U61(tt, U21(tt, x1)) -> c26(A__LENGTH(a__U21(tt, x1)), MARK(U21(tt, x1))) A__U61(tt, U21(s(z0), x1)) -> c26(A__LENGTH(a__U21(s(mark(z0)), x1)), MARK(U21(s(z0), x1))) A__U61(tt, U21(x0, z1)) -> c26(MARK(U21(x0, z1))) A__U61(tt, U21(0, x1)) -> c26(A__LENGTH(a__U21(0, x1))) A__U61(tt, U21(nil, x1)) -> c26(A__LENGTH(a__U21(nil, x1))) A__U61(tt, U22(zeros)) -> c26(A__LENGTH(a__U22(a__zeros)), MARK(U22(zeros))) A__U61(tt, U22(U11(z0, z1))) -> c26(A__LENGTH(a__U22(a__U11(mark(z0), z1))), MARK(U22(U11(z0, z1)))) A__U61(tt, U22(U12(z0))) -> c26(A__LENGTH(a__U22(a__U12(mark(z0)))), MARK(U22(U12(z0)))) A__U61(tt, U22(isNatList(z0))) -> c26(A__LENGTH(a__U22(a__isNatList(z0))), MARK(U22(isNatList(z0)))) A__U61(tt, U22(U21(z0, z1))) -> c26(A__LENGTH(a__U22(a__U21(mark(z0), z1))), MARK(U22(U21(z0, z1)))) A__U61(tt, U22(U22(z0))) -> c26(A__LENGTH(a__U22(a__U22(mark(z0)))), MARK(U22(U22(z0)))) A__U61(tt, U22(isNat(z0))) -> c26(A__LENGTH(a__U22(a__isNat(z0))), MARK(U22(isNat(z0)))) A__U61(tt, U22(U31(z0, z1))) -> c26(A__LENGTH(a__U22(a__U31(mark(z0), z1))), MARK(U22(U31(z0, z1)))) A__U61(tt, U22(U32(z0))) -> c26(A__LENGTH(a__U22(a__U32(mark(z0)))), MARK(U22(U32(z0)))) A__U61(tt, U22(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U22(a__U41(mark(z0), z1, z2))), MARK(U22(U41(z0, z1, z2)))) A__U61(tt, U22(U42(z0, z1))) -> c26(A__LENGTH(a__U22(a__U42(mark(z0), z1))), MARK(U22(U42(z0, z1)))) A__U61(tt, U22(U43(z0))) -> c26(A__LENGTH(a__U22(a__U43(mark(z0)))), MARK(U22(U43(z0)))) A__U61(tt, U22(isNatIList(z0))) -> c26(A__LENGTH(a__U22(a__isNatIList(z0))), MARK(U22(isNatIList(z0)))) A__U61(tt, U22(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U22(a__U51(mark(z0), z1, z2))), MARK(U22(U51(z0, z1, z2)))) A__U61(tt, U22(U52(z0, z1))) -> c26(A__LENGTH(a__U22(a__U52(mark(z0), z1))), MARK(U22(U52(z0, z1)))) A__U61(tt, U22(U53(z0))) -> c26(A__LENGTH(a__U22(a__U53(mark(z0)))), MARK(U22(U53(z0)))) A__U61(tt, U22(U61(z0, z1))) -> c26(A__LENGTH(a__U22(a__U61(mark(z0), z1))), MARK(U22(U61(z0, z1)))) A__U61(tt, U22(length(z0))) -> c26(A__LENGTH(a__U22(a__length(mark(z0)))), MARK(U22(length(z0)))) A__U61(tt, U22(and(z0, z1))) -> c26(A__LENGTH(a__U22(a__and(mark(z0), z1))), MARK(U22(and(z0, z1)))) A__U61(tt, U22(isNatIListKind(z0))) -> c26(A__LENGTH(a__U22(a__isNatIListKind(z0))), MARK(U22(isNatIListKind(z0)))) A__U61(tt, U22(isNatKind(z0))) -> c26(A__LENGTH(a__U22(a__isNatKind(z0))), MARK(U22(isNatKind(z0)))) A__U61(tt, U22(cons(z0, z1))) -> c26(A__LENGTH(a__U22(cons(mark(z0), z1))), MARK(U22(cons(z0, z1)))) A__U61(tt, U22(0)) -> c26(A__LENGTH(a__U22(0)), MARK(U22(0))) A__U61(tt, U22(tt)) -> c26(A__LENGTH(a__U22(tt)), MARK(U22(tt))) A__U61(tt, U22(s(z0))) -> c26(A__LENGTH(a__U22(s(mark(z0)))), MARK(U22(s(z0)))) A__U61(tt, U22(nil)) -> c26(A__LENGTH(a__U22(nil)), MARK(U22(nil))) A__U61(tt, U22(x0)) -> c26(MARK(U22(x0))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> c26(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U61(tt, U12(U21(z0, z1))) -> c26(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U61(tt, U12(U22(z0))) -> c26(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U61(tt, U12(isNat(z0))) -> c26(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U61(tt, U12(U31(z0, z1))) -> c26(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U61(tt, U12(U32(z0))) -> c26(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U61(tt, U12(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U61(tt, U12(U42(z0, z1))) -> c26(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U61(tt, U12(U43(z0))) -> c26(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U61(tt, U12(isNatIList(z0))) -> c26(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U61(tt, U12(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U61(tt, U12(U52(z0, z1))) -> c26(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U61(tt, U12(U53(z0))) -> c26(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U61(tt, U12(U61(z0, z1))) -> c26(A__LENGTH(a__U12(a__U61(mark(z0), z1))), MARK(U12(U61(z0, z1)))) A__U61(tt, U12(length(z0))) -> c26(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U61(tt, U12(and(z0, z1))) -> c26(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U61(tt, U12(isNatIListKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U61(tt, U12(isNatKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U61(tt, U12(cons(z0, z1))) -> c26(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U61(tt, U12(0)) -> c26(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U61(tt, U12(tt)) -> c26(A__LENGTH(a__U12(tt)), MARK(U12(tt))) A__U61(tt, U12(s(z0))) -> c26(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U61(tt, U12(nil)) -> c26(A__LENGTH(a__U12(nil)), MARK(U12(nil))) A__U61(tt, U12(x0)) -> c26(MARK(U12(x0))) A__U61(tt, isNatList(cons(z0, z1))) -> c26(A__LENGTH(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(cons(z0, z1)))) A__U61(tt, isNatList(nil)) -> c26(MARK(isNatList(nil))) A__U61(tt, isNatList(z0)) -> c26(MARK(isNatList(z0))) A__U61(tt, U21(zeros, x1)) -> c26(A__LENGTH(a__U21(a__zeros, x1)), MARK(U21(zeros, x1))) A__U61(tt, U21(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1)), MARK(U21(U11(z0, z1), x1))) A__U61(tt, U21(U12(z0), x1)) -> c26(A__LENGTH(a__U21(a__U12(mark(z0)), x1)), MARK(U21(U12(z0), x1))) A__U61(tt, U21(isNatList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatList(z0), x1)), MARK(U21(isNatList(z0), x1))) A__U61(tt, U21(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U21(mark(z0), z1), x1)), MARK(U21(U21(z0, z1), x1))) A__U61(tt, U21(U22(z0), x1)) -> c26(A__LENGTH(a__U21(a__U22(mark(z0)), x1)), MARK(U21(U22(z0), x1))) A__U61(tt, U21(isNat(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNat(z0), x1)), MARK(U21(isNat(z0), x1))) A__U61(tt, U21(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U31(mark(z0), z1), x1)), MARK(U21(U31(z0, z1), x1))) A__U61(tt, U21(U32(z0), x1)) -> c26(A__LENGTH(a__U21(a__U32(mark(z0)), x1)), MARK(U21(U32(z0), x1))) A__U61(tt, U21(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(U21(U41(z0, z1, z2), x1))) A__U61(tt, U21(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U42(mark(z0), z1), x1)), MARK(U21(U42(z0, z1), x1))) A__U61(tt, U21(U43(z0), x1)) -> c26(A__LENGTH(a__U21(a__U43(mark(z0)), x1)), MARK(U21(U43(z0), x1))) A__U61(tt, U21(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIList(z0), x1)), MARK(U21(isNatIList(z0), x1))) A__U61(tt, U21(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U51(mark(z0), z1, z2), x1)), MARK(U21(U51(z0, z1, z2), x1))) A__U61(tt, U21(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U52(mark(z0), z1), x1)), MARK(U21(U52(z0, z1), x1))) A__U61(tt, U21(U53(z0), x1)) -> c26(A__LENGTH(a__U21(a__U53(mark(z0)), x1)), MARK(U21(U53(z0), x1))) A__U61(tt, U21(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U61(mark(z0), z1), x1)), MARK(U21(U61(z0, z1), x1))) A__U61(tt, U21(length(z0), x1)) -> c26(A__LENGTH(a__U21(a__length(mark(z0)), x1)), MARK(U21(length(z0), x1))) A__U61(tt, U21(and(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__and(mark(z0), z1), x1)), MARK(U21(and(z0, z1), x1))) A__U61(tt, U21(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIListKind(z0), x1)), MARK(U21(isNatIListKind(z0), x1))) A__U61(tt, U21(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), x1)), MARK(U21(isNatKind(z0), x1))) A__U61(tt, U21(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U21(cons(mark(z0), z1), x1)), MARK(U21(cons(z0, z1), x1))) A__U61(tt, U21(tt, x1)) -> c26(A__LENGTH(a__U21(tt, x1)), MARK(U21(tt, x1))) A__U61(tt, U21(s(z0), x1)) -> c26(A__LENGTH(a__U21(s(mark(z0)), x1)), MARK(U21(s(z0), x1))) A__U61(tt, U21(x0, z1)) -> c26(MARK(U21(x0, z1))) A__U61(tt, U21(0, x1)) -> c26(A__LENGTH(a__U21(0, x1))) A__U61(tt, U21(nil, x1)) -> c26(A__LENGTH(a__U21(nil, x1))) A__U61(tt, U22(zeros)) -> c26(A__LENGTH(a__U22(a__zeros)), MARK(U22(zeros))) A__U61(tt, U22(U11(z0, z1))) -> c26(A__LENGTH(a__U22(a__U11(mark(z0), z1))), MARK(U22(U11(z0, z1)))) A__U61(tt, U22(U12(z0))) -> c26(A__LENGTH(a__U22(a__U12(mark(z0)))), MARK(U22(U12(z0)))) A__U61(tt, U22(isNatList(z0))) -> c26(A__LENGTH(a__U22(a__isNatList(z0))), MARK(U22(isNatList(z0)))) A__U61(tt, U22(U21(z0, z1))) -> c26(A__LENGTH(a__U22(a__U21(mark(z0), z1))), MARK(U22(U21(z0, z1)))) A__U61(tt, U22(U22(z0))) -> c26(A__LENGTH(a__U22(a__U22(mark(z0)))), MARK(U22(U22(z0)))) A__U61(tt, U22(isNat(z0))) -> c26(A__LENGTH(a__U22(a__isNat(z0))), MARK(U22(isNat(z0)))) A__U61(tt, U22(U31(z0, z1))) -> c26(A__LENGTH(a__U22(a__U31(mark(z0), z1))), MARK(U22(U31(z0, z1)))) A__U61(tt, U22(U32(z0))) -> c26(A__LENGTH(a__U22(a__U32(mark(z0)))), MARK(U22(U32(z0)))) A__U61(tt, U22(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U22(a__U41(mark(z0), z1, z2))), MARK(U22(U41(z0, z1, z2)))) A__U61(tt, U22(U42(z0, z1))) -> c26(A__LENGTH(a__U22(a__U42(mark(z0), z1))), MARK(U22(U42(z0, z1)))) A__U61(tt, U22(U43(z0))) -> c26(A__LENGTH(a__U22(a__U43(mark(z0)))), MARK(U22(U43(z0)))) A__U61(tt, U22(isNatIList(z0))) -> c26(A__LENGTH(a__U22(a__isNatIList(z0))), MARK(U22(isNatIList(z0)))) A__U61(tt, U22(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U22(a__U51(mark(z0), z1, z2))), MARK(U22(U51(z0, z1, z2)))) A__U61(tt, U22(U52(z0, z1))) -> c26(A__LENGTH(a__U22(a__U52(mark(z0), z1))), MARK(U22(U52(z0, z1)))) A__U61(tt, U22(U53(z0))) -> c26(A__LENGTH(a__U22(a__U53(mark(z0)))), MARK(U22(U53(z0)))) A__U61(tt, U22(U61(z0, z1))) -> c26(A__LENGTH(a__U22(a__U61(mark(z0), z1))), MARK(U22(U61(z0, z1)))) A__U61(tt, U22(length(z0))) -> c26(A__LENGTH(a__U22(a__length(mark(z0)))), MARK(U22(length(z0)))) A__U61(tt, U22(and(z0, z1))) -> c26(A__LENGTH(a__U22(a__and(mark(z0), z1))), MARK(U22(and(z0, z1)))) A__U61(tt, U22(isNatIListKind(z0))) -> c26(A__LENGTH(a__U22(a__isNatIListKind(z0))), MARK(U22(isNatIListKind(z0)))) A__U61(tt, U22(isNatKind(z0))) -> c26(A__LENGTH(a__U22(a__isNatKind(z0))), MARK(U22(isNatKind(z0)))) A__U61(tt, U22(cons(z0, z1))) -> c26(A__LENGTH(a__U22(cons(mark(z0), z1))), MARK(U22(cons(z0, z1)))) A__U61(tt, U22(0)) -> c26(A__LENGTH(a__U22(0)), MARK(U22(0))) A__U61(tt, U22(tt)) -> c26(A__LENGTH(a__U22(tt)), MARK(U22(tt))) A__U61(tt, U22(s(z0))) -> c26(A__LENGTH(a__U22(s(mark(z0)))), MARK(U22(s(z0)))) A__U61(tt, U22(nil)) -> c26(A__LENGTH(a__U22(nil)), MARK(U22(nil))) A__U61(tt, U22(x0)) -> c26(MARK(U22(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_1, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c14_2, c20_2 ---------------------------------------- (167) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U61(tt, isNat(z0)) -> c26(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) by A__U61(tt, isNat(0)) -> c26(A__LENGTH(tt), MARK(isNat(0))) A__U61(tt, isNat(length(z0))) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), z0)), MARK(isNat(length(z0)))) A__U61(tt, isNat(s(z0))) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), z0)), MARK(isNat(s(z0)))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(isNat(z0)), MARK(isNat(z0))) ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) 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c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> c26(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U61(tt, U12(U21(z0, z1))) -> c26(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U61(tt, U12(U22(z0))) -> c26(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U61(tt, U12(isNat(z0))) -> c26(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U61(tt, U12(U31(z0, z1))) -> c26(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U61(tt, U12(U32(z0))) -> c26(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U61(tt, U12(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U61(tt, U12(U42(z0, z1))) -> c26(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U61(tt, U12(U43(z0))) -> c26(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U61(tt, U12(isNatIList(z0))) -> c26(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U61(tt, U12(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U61(tt, U12(U52(z0, z1))) -> c26(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U61(tt, U12(U53(z0))) -> c26(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U61(tt, U12(U61(z0, z1))) -> c26(A__LENGTH(a__U12(a__U61(mark(z0), z1))), MARK(U12(U61(z0, z1)))) A__U61(tt, U12(length(z0))) -> c26(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U61(tt, U12(and(z0, z1))) -> c26(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U61(tt, U12(isNatIListKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U61(tt, U12(isNatKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U61(tt, U12(cons(z0, z1))) -> c26(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U61(tt, U12(0)) -> c26(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U61(tt, U12(tt)) -> c26(A__LENGTH(a__U12(tt)), MARK(U12(tt))) A__U61(tt, U12(s(z0))) -> c26(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U61(tt, U12(nil)) -> c26(A__LENGTH(a__U12(nil)), MARK(U12(nil))) A__U61(tt, U12(x0)) -> c26(MARK(U12(x0))) A__U61(tt, isNatList(cons(z0, z1))) -> c26(A__LENGTH(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(cons(z0, z1)))) A__U61(tt, isNatList(nil)) -> c26(MARK(isNatList(nil))) A__U61(tt, isNatList(z0)) -> c26(MARK(isNatList(z0))) A__U61(tt, U21(zeros, x1)) -> c26(A__LENGTH(a__U21(a__zeros, x1)), MARK(U21(zeros, x1))) A__U61(tt, U21(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1)), MARK(U21(U11(z0, z1), x1))) A__U61(tt, U21(U12(z0), x1)) -> c26(A__LENGTH(a__U21(a__U12(mark(z0)), x1)), MARK(U21(U12(z0), x1))) A__U61(tt, U21(isNatList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatList(z0), x1)), MARK(U21(isNatList(z0), x1))) A__U61(tt, U21(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U21(mark(z0), z1), x1)), MARK(U21(U21(z0, z1), x1))) A__U61(tt, U21(U22(z0), x1)) -> c26(A__LENGTH(a__U21(a__U22(mark(z0)), x1)), MARK(U21(U22(z0), x1))) A__U61(tt, U21(isNat(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNat(z0), x1)), MARK(U21(isNat(z0), x1))) A__U61(tt, U21(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U31(mark(z0), z1), x1)), MARK(U21(U31(z0, z1), x1))) A__U61(tt, U21(U32(z0), x1)) -> c26(A__LENGTH(a__U21(a__U32(mark(z0)), x1)), MARK(U21(U32(z0), x1))) A__U61(tt, U21(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(U21(U41(z0, z1, z2), x1))) A__U61(tt, U21(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U42(mark(z0), z1), x1)), MARK(U21(U42(z0, z1), x1))) A__U61(tt, U21(U43(z0), x1)) -> c26(A__LENGTH(a__U21(a__U43(mark(z0)), x1)), MARK(U21(U43(z0), x1))) A__U61(tt, U21(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIList(z0), x1)), MARK(U21(isNatIList(z0), x1))) A__U61(tt, U21(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U51(mark(z0), z1, z2), x1)), MARK(U21(U51(z0, z1, z2), x1))) A__U61(tt, U21(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U52(mark(z0), z1), x1)), MARK(U21(U52(z0, z1), x1))) A__U61(tt, U21(U53(z0), x1)) -> c26(A__LENGTH(a__U21(a__U53(mark(z0)), x1)), MARK(U21(U53(z0), x1))) A__U61(tt, U21(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U61(mark(z0), z1), x1)), MARK(U21(U61(z0, z1), x1))) A__U61(tt, U21(length(z0), x1)) -> c26(A__LENGTH(a__U21(a__length(mark(z0)), x1)), MARK(U21(length(z0), x1))) A__U61(tt, U21(and(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__and(mark(z0), z1), x1)), MARK(U21(and(z0, z1), x1))) A__U61(tt, U21(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIListKind(z0), x1)), MARK(U21(isNatIListKind(z0), x1))) A__U61(tt, U21(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), x1)), MARK(U21(isNatKind(z0), x1))) A__U61(tt, U21(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U21(cons(mark(z0), z1), x1)), MARK(U21(cons(z0, z1), x1))) A__U61(tt, U21(tt, x1)) -> c26(A__LENGTH(a__U21(tt, x1)), MARK(U21(tt, x1))) A__U61(tt, U21(s(z0), x1)) -> c26(A__LENGTH(a__U21(s(mark(z0)), x1)), MARK(U21(s(z0), x1))) A__U61(tt, U21(x0, z1)) -> c26(MARK(U21(x0, z1))) A__U61(tt, U21(0, x1)) -> c26(A__LENGTH(a__U21(0, x1))) A__U61(tt, U21(nil, x1)) -> c26(A__LENGTH(a__U21(nil, x1))) A__U61(tt, U22(zeros)) -> c26(A__LENGTH(a__U22(a__zeros)), MARK(U22(zeros))) A__U61(tt, U22(U11(z0, z1))) -> c26(A__LENGTH(a__U22(a__U11(mark(z0), z1))), MARK(U22(U11(z0, z1)))) A__U61(tt, U22(U12(z0))) -> c26(A__LENGTH(a__U22(a__U12(mark(z0)))), MARK(U22(U12(z0)))) A__U61(tt, U22(isNatList(z0))) -> c26(A__LENGTH(a__U22(a__isNatList(z0))), MARK(U22(isNatList(z0)))) A__U61(tt, U22(U21(z0, z1))) -> c26(A__LENGTH(a__U22(a__U21(mark(z0), z1))), MARK(U22(U21(z0, z1)))) A__U61(tt, U22(U22(z0))) -> c26(A__LENGTH(a__U22(a__U22(mark(z0)))), MARK(U22(U22(z0)))) A__U61(tt, U22(isNat(z0))) -> c26(A__LENGTH(a__U22(a__isNat(z0))), MARK(U22(isNat(z0)))) A__U61(tt, U22(U31(z0, z1))) -> c26(A__LENGTH(a__U22(a__U31(mark(z0), z1))), MARK(U22(U31(z0, z1)))) A__U61(tt, U22(U32(z0))) -> c26(A__LENGTH(a__U22(a__U32(mark(z0)))), MARK(U22(U32(z0)))) A__U61(tt, U22(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U22(a__U41(mark(z0), z1, z2))), MARK(U22(U41(z0, z1, z2)))) A__U61(tt, U22(U42(z0, z1))) -> c26(A__LENGTH(a__U22(a__U42(mark(z0), z1))), MARK(U22(U42(z0, z1)))) A__U61(tt, U22(U43(z0))) -> c26(A__LENGTH(a__U22(a__U43(mark(z0)))), MARK(U22(U43(z0)))) A__U61(tt, U22(isNatIList(z0))) -> c26(A__LENGTH(a__U22(a__isNatIList(z0))), MARK(U22(isNatIList(z0)))) A__U61(tt, U22(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U22(a__U51(mark(z0), z1, z2))), MARK(U22(U51(z0, z1, z2)))) A__U61(tt, U22(U52(z0, z1))) -> c26(A__LENGTH(a__U22(a__U52(mark(z0), z1))), MARK(U22(U52(z0, z1)))) A__U61(tt, U22(U53(z0))) -> c26(A__LENGTH(a__U22(a__U53(mark(z0)))), MARK(U22(U53(z0)))) A__U61(tt, U22(U61(z0, z1))) -> c26(A__LENGTH(a__U22(a__U61(mark(z0), z1))), MARK(U22(U61(z0, z1)))) A__U61(tt, U22(length(z0))) -> c26(A__LENGTH(a__U22(a__length(mark(z0)))), MARK(U22(length(z0)))) A__U61(tt, U22(and(z0, z1))) -> c26(A__LENGTH(a__U22(a__and(mark(z0), z1))), MARK(U22(and(z0, z1)))) A__U61(tt, U22(isNatIListKind(z0))) -> c26(A__LENGTH(a__U22(a__isNatIListKind(z0))), MARK(U22(isNatIListKind(z0)))) A__U61(tt, U22(isNatKind(z0))) -> c26(A__LENGTH(a__U22(a__isNatKind(z0))), MARK(U22(isNatKind(z0)))) A__U61(tt, U22(cons(z0, z1))) -> c26(A__LENGTH(a__U22(cons(mark(z0), z1))), MARK(U22(cons(z0, z1)))) A__U61(tt, U22(0)) -> c26(A__LENGTH(a__U22(0)), MARK(U22(0))) A__U61(tt, U22(tt)) -> c26(A__LENGTH(a__U22(tt)), MARK(U22(tt))) A__U61(tt, U22(s(z0))) -> c26(A__LENGTH(a__U22(s(mark(z0)))), MARK(U22(s(z0)))) A__U61(tt, U22(nil)) -> c26(A__LENGTH(a__U22(nil)), MARK(U22(nil))) A__U61(tt, U22(x0)) -> c26(MARK(U22(x0))) A__U61(tt, isNat(0)) -> c26(A__LENGTH(tt), MARK(isNat(0))) A__U61(tt, isNat(length(z0))) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), z0)), MARK(isNat(length(z0)))) A__U61(tt, isNat(s(z0))) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), z0)), MARK(isNat(s(z0)))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(isNat(z0)), MARK(isNat(z0))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> c26(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U61(tt, U12(U21(z0, z1))) -> c26(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U61(tt, U12(U22(z0))) -> c26(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U61(tt, U12(isNat(z0))) -> c26(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U61(tt, U12(U31(z0, z1))) -> c26(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U61(tt, U12(U32(z0))) -> c26(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U61(tt, U12(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U61(tt, U12(U42(z0, z1))) -> c26(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U61(tt, U12(U43(z0))) -> c26(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U61(tt, U12(isNatIList(z0))) -> c26(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U61(tt, U12(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U61(tt, U12(U52(z0, z1))) -> c26(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U61(tt, U12(U53(z0))) -> c26(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U61(tt, U12(U61(z0, z1))) -> c26(A__LENGTH(a__U12(a__U61(mark(z0), z1))), MARK(U12(U61(z0, z1)))) A__U61(tt, U12(length(z0))) -> c26(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U61(tt, U12(and(z0, z1))) -> c26(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U61(tt, U12(isNatIListKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U61(tt, U12(isNatKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U61(tt, U12(cons(z0, z1))) -> c26(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U61(tt, U12(0)) -> c26(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U61(tt, U12(tt)) -> c26(A__LENGTH(a__U12(tt)), MARK(U12(tt))) A__U61(tt, U12(s(z0))) -> c26(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U61(tt, U12(nil)) -> c26(A__LENGTH(a__U12(nil)), MARK(U12(nil))) A__U61(tt, U12(x0)) -> c26(MARK(U12(x0))) A__U61(tt, isNatList(cons(z0, z1))) -> c26(A__LENGTH(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(cons(z0, z1)))) A__U61(tt, isNatList(nil)) -> c26(MARK(isNatList(nil))) A__U61(tt, isNatList(z0)) -> c26(MARK(isNatList(z0))) A__U61(tt, U21(zeros, x1)) -> c26(A__LENGTH(a__U21(a__zeros, x1)), MARK(U21(zeros, x1))) A__U61(tt, U21(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1)), MARK(U21(U11(z0, z1), x1))) A__U61(tt, U21(U12(z0), x1)) -> c26(A__LENGTH(a__U21(a__U12(mark(z0)), x1)), MARK(U21(U12(z0), x1))) A__U61(tt, U21(isNatList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatList(z0), x1)), MARK(U21(isNatList(z0), x1))) A__U61(tt, U21(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U21(mark(z0), z1), x1)), MARK(U21(U21(z0, z1), x1))) A__U61(tt, U21(U22(z0), x1)) -> c26(A__LENGTH(a__U21(a__U22(mark(z0)), x1)), MARK(U21(U22(z0), x1))) A__U61(tt, U21(isNat(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNat(z0), x1)), MARK(U21(isNat(z0), x1))) A__U61(tt, U21(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U31(mark(z0), z1), x1)), MARK(U21(U31(z0, z1), x1))) A__U61(tt, U21(U32(z0), x1)) -> c26(A__LENGTH(a__U21(a__U32(mark(z0)), x1)), MARK(U21(U32(z0), x1))) A__U61(tt, U21(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(U21(U41(z0, z1, z2), x1))) A__U61(tt, U21(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U42(mark(z0), z1), x1)), MARK(U21(U42(z0, z1), x1))) A__U61(tt, U21(U43(z0), x1)) -> c26(A__LENGTH(a__U21(a__U43(mark(z0)), x1)), MARK(U21(U43(z0), x1))) A__U61(tt, U21(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIList(z0), x1)), MARK(U21(isNatIList(z0), x1))) A__U61(tt, U21(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U51(mark(z0), z1, z2), x1)), MARK(U21(U51(z0, z1, z2), x1))) A__U61(tt, U21(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U52(mark(z0), z1), x1)), MARK(U21(U52(z0, z1), x1))) A__U61(tt, U21(U53(z0), x1)) -> c26(A__LENGTH(a__U21(a__U53(mark(z0)), x1)), MARK(U21(U53(z0), x1))) A__U61(tt, U21(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U61(mark(z0), z1), x1)), MARK(U21(U61(z0, z1), x1))) A__U61(tt, U21(length(z0), x1)) -> c26(A__LENGTH(a__U21(a__length(mark(z0)), x1)), MARK(U21(length(z0), x1))) A__U61(tt, U21(and(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__and(mark(z0), z1), x1)), MARK(U21(and(z0, z1), x1))) A__U61(tt, U21(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIListKind(z0), x1)), MARK(U21(isNatIListKind(z0), x1))) A__U61(tt, U21(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), x1)), MARK(U21(isNatKind(z0), x1))) A__U61(tt, U21(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U21(cons(mark(z0), z1), x1)), MARK(U21(cons(z0, z1), x1))) A__U61(tt, U21(tt, x1)) -> c26(A__LENGTH(a__U21(tt, x1)), MARK(U21(tt, x1))) A__U61(tt, U21(s(z0), x1)) -> c26(A__LENGTH(a__U21(s(mark(z0)), x1)), MARK(U21(s(z0), x1))) A__U61(tt, U21(x0, z1)) -> c26(MARK(U21(x0, z1))) A__U61(tt, U21(0, x1)) -> c26(A__LENGTH(a__U21(0, x1))) A__U61(tt, U21(nil, x1)) -> c26(A__LENGTH(a__U21(nil, x1))) A__U61(tt, U22(zeros)) -> c26(A__LENGTH(a__U22(a__zeros)), MARK(U22(zeros))) A__U61(tt, U22(U11(z0, z1))) -> c26(A__LENGTH(a__U22(a__U11(mark(z0), z1))), MARK(U22(U11(z0, z1)))) A__U61(tt, U22(U12(z0))) -> c26(A__LENGTH(a__U22(a__U12(mark(z0)))), MARK(U22(U12(z0)))) A__U61(tt, U22(isNatList(z0))) -> c26(A__LENGTH(a__U22(a__isNatList(z0))), MARK(U22(isNatList(z0)))) A__U61(tt, U22(U21(z0, z1))) -> c26(A__LENGTH(a__U22(a__U21(mark(z0), z1))), MARK(U22(U21(z0, z1)))) A__U61(tt, U22(U22(z0))) -> c26(A__LENGTH(a__U22(a__U22(mark(z0)))), MARK(U22(U22(z0)))) A__U61(tt, U22(isNat(z0))) -> c26(A__LENGTH(a__U22(a__isNat(z0))), MARK(U22(isNat(z0)))) A__U61(tt, U22(U31(z0, z1))) -> c26(A__LENGTH(a__U22(a__U31(mark(z0), z1))), MARK(U22(U31(z0, z1)))) A__U61(tt, U22(U32(z0))) -> c26(A__LENGTH(a__U22(a__U32(mark(z0)))), MARK(U22(U32(z0)))) A__U61(tt, U22(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U22(a__U41(mark(z0), z1, z2))), MARK(U22(U41(z0, z1, z2)))) A__U61(tt, U22(U42(z0, z1))) -> c26(A__LENGTH(a__U22(a__U42(mark(z0), z1))), MARK(U22(U42(z0, z1)))) A__U61(tt, U22(U43(z0))) -> c26(A__LENGTH(a__U22(a__U43(mark(z0)))), MARK(U22(U43(z0)))) A__U61(tt, U22(isNatIList(z0))) -> c26(A__LENGTH(a__U22(a__isNatIList(z0))), MARK(U22(isNatIList(z0)))) A__U61(tt, U22(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U22(a__U51(mark(z0), z1, z2))), MARK(U22(U51(z0, z1, z2)))) A__U61(tt, U22(U52(z0, z1))) -> c26(A__LENGTH(a__U22(a__U52(mark(z0), z1))), MARK(U22(U52(z0, z1)))) A__U61(tt, U22(U53(z0))) -> c26(A__LENGTH(a__U22(a__U53(mark(z0)))), MARK(U22(U53(z0)))) A__U61(tt, U22(U61(z0, z1))) -> c26(A__LENGTH(a__U22(a__U61(mark(z0), z1))), MARK(U22(U61(z0, z1)))) A__U61(tt, U22(length(z0))) -> c26(A__LENGTH(a__U22(a__length(mark(z0)))), MARK(U22(length(z0)))) A__U61(tt, U22(and(z0, z1))) -> c26(A__LENGTH(a__U22(a__and(mark(z0), z1))), MARK(U22(and(z0, z1)))) A__U61(tt, U22(isNatIListKind(z0))) -> c26(A__LENGTH(a__U22(a__isNatIListKind(z0))), MARK(U22(isNatIListKind(z0)))) A__U61(tt, U22(isNatKind(z0))) -> c26(A__LENGTH(a__U22(a__isNatKind(z0))), MARK(U22(isNatKind(z0)))) A__U61(tt, U22(cons(z0, z1))) -> c26(A__LENGTH(a__U22(cons(mark(z0), z1))), MARK(U22(cons(z0, z1)))) A__U61(tt, U22(0)) -> c26(A__LENGTH(a__U22(0)), MARK(U22(0))) A__U61(tt, U22(tt)) -> c26(A__LENGTH(a__U22(tt)), MARK(U22(tt))) A__U61(tt, U22(s(z0))) -> c26(A__LENGTH(a__U22(s(mark(z0)))), MARK(U22(s(z0)))) A__U61(tt, U22(nil)) -> c26(A__LENGTH(a__U22(nil)), MARK(U22(nil))) A__U61(tt, U22(x0)) -> c26(MARK(U22(x0))) A__U61(tt, isNat(0)) -> c26(A__LENGTH(tt), MARK(isNat(0))) A__U61(tt, isNat(length(z0))) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), z0)), MARK(isNat(length(z0)))) A__U61(tt, isNat(s(z0))) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), z0)), MARK(isNat(s(z0)))) A__U61(tt, isNat(z0)) -> c26(A__LENGTH(isNat(z0)), MARK(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_1, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c14_2, c20_2 ---------------------------------------- (169) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> c26(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U61(tt, U12(U21(z0, z1))) -> c26(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U61(tt, U12(U22(z0))) -> c26(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U61(tt, U12(isNat(z0))) -> c26(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U61(tt, U12(U31(z0, z1))) -> c26(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U61(tt, U12(U32(z0))) -> c26(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U61(tt, U12(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U61(tt, U12(U42(z0, z1))) -> c26(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U61(tt, U12(U43(z0))) -> c26(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U61(tt, U12(isNatIList(z0))) -> c26(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U61(tt, U12(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U61(tt, U12(U52(z0, z1))) -> c26(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U61(tt, U12(U53(z0))) -> c26(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U61(tt, U12(U61(z0, z1))) -> c26(A__LENGTH(a__U12(a__U61(mark(z0), z1))), MARK(U12(U61(z0, z1)))) A__U61(tt, U12(length(z0))) -> c26(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U61(tt, U12(and(z0, z1))) -> c26(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U61(tt, U12(isNatIListKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U61(tt, U12(isNatKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U61(tt, U12(cons(z0, z1))) -> c26(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U61(tt, U12(0)) -> c26(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U61(tt, U12(tt)) -> c26(A__LENGTH(a__U12(tt)), MARK(U12(tt))) A__U61(tt, U12(s(z0))) -> c26(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U61(tt, U12(nil)) -> c26(A__LENGTH(a__U12(nil)), MARK(U12(nil))) A__U61(tt, U12(x0)) -> c26(MARK(U12(x0))) A__U61(tt, isNatList(cons(z0, z1))) -> c26(A__LENGTH(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(cons(z0, z1)))) A__U61(tt, isNatList(nil)) -> c26(MARK(isNatList(nil))) A__U61(tt, isNatList(z0)) -> c26(MARK(isNatList(z0))) A__U61(tt, U21(zeros, x1)) -> c26(A__LENGTH(a__U21(a__zeros, x1)), MARK(U21(zeros, x1))) A__U61(tt, U21(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1)), MARK(U21(U11(z0, z1), x1))) A__U61(tt, U21(U12(z0), x1)) -> c26(A__LENGTH(a__U21(a__U12(mark(z0)), x1)), MARK(U21(U12(z0), x1))) A__U61(tt, U21(isNatList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatList(z0), x1)), MARK(U21(isNatList(z0), x1))) A__U61(tt, U21(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U21(mark(z0), z1), x1)), MARK(U21(U21(z0, z1), x1))) A__U61(tt, U21(U22(z0), x1)) -> c26(A__LENGTH(a__U21(a__U22(mark(z0)), x1)), MARK(U21(U22(z0), x1))) A__U61(tt, U21(isNat(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNat(z0), x1)), MARK(U21(isNat(z0), x1))) A__U61(tt, U21(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U31(mark(z0), z1), x1)), MARK(U21(U31(z0, z1), x1))) A__U61(tt, U21(U32(z0), x1)) -> c26(A__LENGTH(a__U21(a__U32(mark(z0)), x1)), MARK(U21(U32(z0), x1))) A__U61(tt, U21(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(U21(U41(z0, z1, z2), x1))) A__U61(tt, U21(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U42(mark(z0), z1), x1)), MARK(U21(U42(z0, z1), x1))) A__U61(tt, U21(U43(z0), x1)) -> c26(A__LENGTH(a__U21(a__U43(mark(z0)), x1)), MARK(U21(U43(z0), x1))) A__U61(tt, U21(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIList(z0), x1)), MARK(U21(isNatIList(z0), x1))) A__U61(tt, U21(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U51(mark(z0), z1, z2), x1)), MARK(U21(U51(z0, z1, z2), x1))) A__U61(tt, U21(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U52(mark(z0), z1), x1)), MARK(U21(U52(z0, z1), x1))) A__U61(tt, U21(U53(z0), x1)) -> c26(A__LENGTH(a__U21(a__U53(mark(z0)), x1)), MARK(U21(U53(z0), x1))) A__U61(tt, U21(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U61(mark(z0), z1), x1)), MARK(U21(U61(z0, z1), x1))) A__U61(tt, U21(length(z0), x1)) -> c26(A__LENGTH(a__U21(a__length(mark(z0)), x1)), MARK(U21(length(z0), x1))) A__U61(tt, U21(and(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__and(mark(z0), z1), x1)), MARK(U21(and(z0, z1), x1))) A__U61(tt, U21(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIListKind(z0), x1)), MARK(U21(isNatIListKind(z0), x1))) A__U61(tt, U21(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), x1)), MARK(U21(isNatKind(z0), x1))) A__U61(tt, U21(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U21(cons(mark(z0), z1), x1)), MARK(U21(cons(z0, z1), x1))) A__U61(tt, U21(tt, x1)) -> c26(A__LENGTH(a__U21(tt, x1)), MARK(U21(tt, x1))) A__U61(tt, U21(s(z0), x1)) -> c26(A__LENGTH(a__U21(s(mark(z0)), x1)), MARK(U21(s(z0), x1))) A__U61(tt, U21(x0, z1)) -> c26(MARK(U21(x0, z1))) A__U61(tt, U21(0, x1)) -> c26(A__LENGTH(a__U21(0, x1))) A__U61(tt, U21(nil, x1)) -> c26(A__LENGTH(a__U21(nil, x1))) A__U61(tt, U22(zeros)) -> c26(A__LENGTH(a__U22(a__zeros)), MARK(U22(zeros))) A__U61(tt, U22(U11(z0, z1))) -> c26(A__LENGTH(a__U22(a__U11(mark(z0), z1))), MARK(U22(U11(z0, z1)))) A__U61(tt, U22(U12(z0))) -> c26(A__LENGTH(a__U22(a__U12(mark(z0)))), MARK(U22(U12(z0)))) A__U61(tt, U22(isNatList(z0))) -> c26(A__LENGTH(a__U22(a__isNatList(z0))), MARK(U22(isNatList(z0)))) A__U61(tt, U22(U21(z0, z1))) -> c26(A__LENGTH(a__U22(a__U21(mark(z0), z1))), MARK(U22(U21(z0, z1)))) A__U61(tt, U22(U22(z0))) -> c26(A__LENGTH(a__U22(a__U22(mark(z0)))), MARK(U22(U22(z0)))) A__U61(tt, U22(isNat(z0))) -> c26(A__LENGTH(a__U22(a__isNat(z0))), MARK(U22(isNat(z0)))) A__U61(tt, U22(U31(z0, z1))) -> c26(A__LENGTH(a__U22(a__U31(mark(z0), z1))), MARK(U22(U31(z0, z1)))) A__U61(tt, U22(U32(z0))) -> c26(A__LENGTH(a__U22(a__U32(mark(z0)))), MARK(U22(U32(z0)))) A__U61(tt, U22(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U22(a__U41(mark(z0), z1, z2))), MARK(U22(U41(z0, z1, z2)))) A__U61(tt, U22(U42(z0, z1))) -> c26(A__LENGTH(a__U22(a__U42(mark(z0), z1))), MARK(U22(U42(z0, z1)))) A__U61(tt, U22(U43(z0))) -> c26(A__LENGTH(a__U22(a__U43(mark(z0)))), MARK(U22(U43(z0)))) A__U61(tt, U22(isNatIList(z0))) -> c26(A__LENGTH(a__U22(a__isNatIList(z0))), MARK(U22(isNatIList(z0)))) A__U61(tt, U22(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U22(a__U51(mark(z0), z1, z2))), MARK(U22(U51(z0, z1, z2)))) A__U61(tt, U22(U52(z0, z1))) -> c26(A__LENGTH(a__U22(a__U52(mark(z0), z1))), MARK(U22(U52(z0, z1)))) A__U61(tt, U22(U53(z0))) -> c26(A__LENGTH(a__U22(a__U53(mark(z0)))), MARK(U22(U53(z0)))) A__U61(tt, U22(U61(z0, z1))) -> c26(A__LENGTH(a__U22(a__U61(mark(z0), z1))), MARK(U22(U61(z0, z1)))) A__U61(tt, U22(length(z0))) -> c26(A__LENGTH(a__U22(a__length(mark(z0)))), MARK(U22(length(z0)))) A__U61(tt, U22(and(z0, z1))) -> c26(A__LENGTH(a__U22(a__and(mark(z0), z1))), MARK(U22(and(z0, z1)))) A__U61(tt, U22(isNatIListKind(z0))) -> c26(A__LENGTH(a__U22(a__isNatIListKind(z0))), MARK(U22(isNatIListKind(z0)))) A__U61(tt, U22(isNatKind(z0))) -> c26(A__LENGTH(a__U22(a__isNatKind(z0))), MARK(U22(isNatKind(z0)))) A__U61(tt, U22(cons(z0, z1))) -> c26(A__LENGTH(a__U22(cons(mark(z0), z1))), MARK(U22(cons(z0, z1)))) A__U61(tt, U22(0)) -> c26(A__LENGTH(a__U22(0)), MARK(U22(0))) A__U61(tt, U22(tt)) -> c26(A__LENGTH(a__U22(tt)), MARK(U22(tt))) A__U61(tt, U22(s(z0))) -> c26(A__LENGTH(a__U22(s(mark(z0)))), MARK(U22(s(z0)))) A__U61(tt, U22(nil)) -> c26(A__LENGTH(a__U22(nil)), MARK(U22(nil))) A__U61(tt, U22(x0)) -> c26(MARK(U22(x0))) A__U61(tt, isNat(length(z0))) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), z0)), MARK(isNat(length(z0)))) A__U61(tt, isNat(s(z0))) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), z0)), MARK(isNat(s(z0)))) A__U61(tt, isNat(0)) -> c26(MARK(isNat(0))) A__U61(tt, isNat(z0)) -> c26(MARK(isNat(z0))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, 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c26(A__LENGTH(a__U21(a__U31(mark(z0), z1), x1)), MARK(U21(U31(z0, z1), x1))) A__U61(tt, U21(U32(z0), x1)) -> c26(A__LENGTH(a__U21(a__U32(mark(z0)), x1)), MARK(U21(U32(z0), x1))) A__U61(tt, U21(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(U21(U41(z0, z1, z2), x1))) A__U61(tt, U21(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U42(mark(z0), z1), x1)), MARK(U21(U42(z0, z1), x1))) A__U61(tt, U21(U43(z0), x1)) -> c26(A__LENGTH(a__U21(a__U43(mark(z0)), x1)), MARK(U21(U43(z0), x1))) A__U61(tt, U21(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIList(z0), x1)), MARK(U21(isNatIList(z0), x1))) A__U61(tt, U21(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U51(mark(z0), z1, z2), x1)), MARK(U21(U51(z0, z1, z2), x1))) A__U61(tt, U21(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U52(mark(z0), z1), x1)), MARK(U21(U52(z0, z1), x1))) A__U61(tt, U21(U53(z0), x1)) -> c26(A__LENGTH(a__U21(a__U53(mark(z0)), x1)), MARK(U21(U53(z0), x1))) A__U61(tt, U21(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U61(mark(z0), z1), x1)), MARK(U21(U61(z0, z1), x1))) A__U61(tt, U21(length(z0), x1)) -> c26(A__LENGTH(a__U21(a__length(mark(z0)), x1)), MARK(U21(length(z0), x1))) A__U61(tt, U21(and(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__and(mark(z0), z1), x1)), MARK(U21(and(z0, z1), x1))) A__U61(tt, U21(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIListKind(z0), x1)), MARK(U21(isNatIListKind(z0), x1))) A__U61(tt, U21(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), x1)), MARK(U21(isNatKind(z0), x1))) A__U61(tt, U21(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U21(cons(mark(z0), z1), x1)), MARK(U21(cons(z0, z1), x1))) A__U61(tt, U21(tt, x1)) -> c26(A__LENGTH(a__U21(tt, x1)), MARK(U21(tt, x1))) A__U61(tt, U21(s(z0), x1)) -> c26(A__LENGTH(a__U21(s(mark(z0)), x1)), MARK(U21(s(z0), x1))) A__U61(tt, U21(x0, z1)) -> c26(MARK(U21(x0, z1))) A__U61(tt, U21(0, x1)) -> c26(A__LENGTH(a__U21(0, x1))) A__U61(tt, U21(nil, x1)) -> c26(A__LENGTH(a__U21(nil, x1))) A__U61(tt, U22(zeros)) -> c26(A__LENGTH(a__U22(a__zeros)), MARK(U22(zeros))) A__U61(tt, U22(U11(z0, z1))) -> c26(A__LENGTH(a__U22(a__U11(mark(z0), z1))), MARK(U22(U11(z0, z1)))) A__U61(tt, U22(U12(z0))) -> c26(A__LENGTH(a__U22(a__U12(mark(z0)))), MARK(U22(U12(z0)))) A__U61(tt, U22(isNatList(z0))) -> c26(A__LENGTH(a__U22(a__isNatList(z0))), MARK(U22(isNatList(z0)))) A__U61(tt, U22(U21(z0, z1))) -> c26(A__LENGTH(a__U22(a__U21(mark(z0), z1))), MARK(U22(U21(z0, z1)))) A__U61(tt, U22(U22(z0))) -> c26(A__LENGTH(a__U22(a__U22(mark(z0)))), MARK(U22(U22(z0)))) A__U61(tt, U22(isNat(z0))) -> c26(A__LENGTH(a__U22(a__isNat(z0))), MARK(U22(isNat(z0)))) A__U61(tt, U22(U31(z0, z1))) -> c26(A__LENGTH(a__U22(a__U31(mark(z0), z1))), MARK(U22(U31(z0, z1)))) A__U61(tt, U22(U32(z0))) -> c26(A__LENGTH(a__U22(a__U32(mark(z0)))), MARK(U22(U32(z0)))) A__U61(tt, U22(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U22(a__U41(mark(z0), z1, z2))), MARK(U22(U41(z0, z1, z2)))) A__U61(tt, U22(U42(z0, z1))) -> c26(A__LENGTH(a__U22(a__U42(mark(z0), z1))), MARK(U22(U42(z0, z1)))) A__U61(tt, U22(U43(z0))) -> c26(A__LENGTH(a__U22(a__U43(mark(z0)))), MARK(U22(U43(z0)))) A__U61(tt, U22(isNatIList(z0))) -> c26(A__LENGTH(a__U22(a__isNatIList(z0))), MARK(U22(isNatIList(z0)))) A__U61(tt, U22(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U22(a__U51(mark(z0), z1, z2))), MARK(U22(U51(z0, z1, z2)))) A__U61(tt, U22(U52(z0, z1))) -> c26(A__LENGTH(a__U22(a__U52(mark(z0), z1))), MARK(U22(U52(z0, z1)))) A__U61(tt, U22(U53(z0))) -> c26(A__LENGTH(a__U22(a__U53(mark(z0)))), MARK(U22(U53(z0)))) A__U61(tt, U22(U61(z0, z1))) -> c26(A__LENGTH(a__U22(a__U61(mark(z0), z1))), MARK(U22(U61(z0, z1)))) A__U61(tt, U22(length(z0))) -> c26(A__LENGTH(a__U22(a__length(mark(z0)))), MARK(U22(length(z0)))) A__U61(tt, U22(and(z0, z1))) -> c26(A__LENGTH(a__U22(a__and(mark(z0), z1))), MARK(U22(and(z0, z1)))) A__U61(tt, U22(isNatIListKind(z0))) -> c26(A__LENGTH(a__U22(a__isNatIListKind(z0))), MARK(U22(isNatIListKind(z0)))) A__U61(tt, U22(isNatKind(z0))) -> c26(A__LENGTH(a__U22(a__isNatKind(z0))), MARK(U22(isNatKind(z0)))) A__U61(tt, U22(cons(z0, z1))) -> c26(A__LENGTH(a__U22(cons(mark(z0), z1))), MARK(U22(cons(z0, z1)))) A__U61(tt, U22(0)) -> c26(A__LENGTH(a__U22(0)), MARK(U22(0))) A__U61(tt, U22(tt)) -> c26(A__LENGTH(a__U22(tt)), MARK(U22(tt))) A__U61(tt, U22(s(z0))) -> c26(A__LENGTH(a__U22(s(mark(z0)))), MARK(U22(s(z0)))) A__U61(tt, U22(nil)) -> c26(A__LENGTH(a__U22(nil)), MARK(U22(nil))) A__U61(tt, U22(x0)) -> c26(MARK(U22(x0))) A__U61(tt, isNat(length(z0))) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), z0)), MARK(isNat(length(z0)))) A__U61(tt, isNat(s(z0))) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), z0)), MARK(isNat(s(z0)))) A__U61(tt, isNat(0)) -> c26(MARK(isNat(0))) A__U61(tt, isNat(z0)) -> c26(MARK(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_1, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c14_2, c20_2 ---------------------------------------- (171) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U61(tt, U31(z0, z1)) -> c26(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) by A__U61(tt, U31(x0, z1)) -> c26(A__LENGTH(U31(mark(x0), z1)), MARK(U31(x0, z1))) A__U61(tt, U31(zeros, x1)) -> c26(A__LENGTH(a__U31(a__zeros, x1)), MARK(U31(zeros, x1))) A__U61(tt, U31(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U11(mark(z0), z1), x1)), MARK(U31(U11(z0, z1), x1))) A__U61(tt, U31(U12(z0), x1)) -> c26(A__LENGTH(a__U31(a__U12(mark(z0)), x1)), MARK(U31(U12(z0), x1))) A__U61(tt, U31(isNatList(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatList(z0), x1)), MARK(U31(isNatList(z0), x1))) A__U61(tt, U31(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U21(mark(z0), z1), x1)), MARK(U31(U21(z0, z1), x1))) A__U61(tt, U31(U22(z0), x1)) -> c26(A__LENGTH(a__U31(a__U22(mark(z0)), x1)), MARK(U31(U22(z0), x1))) A__U61(tt, U31(isNat(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNat(z0), x1)), MARK(U31(isNat(z0), x1))) A__U61(tt, U31(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U31(mark(z0), z1), x1)), MARK(U31(U31(z0, z1), x1))) A__U61(tt, U31(U32(z0), x1)) -> c26(A__LENGTH(a__U31(a__U32(mark(z0)), x1)), MARK(U31(U32(z0), x1))) A__U61(tt, U31(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(U31(U41(z0, z1, z2), x1))) A__U61(tt, U31(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U42(mark(z0), z1), x1)), MARK(U31(U42(z0, z1), x1))) A__U61(tt, U31(U43(z0), x1)) -> c26(A__LENGTH(a__U31(a__U43(mark(z0)), x1)), MARK(U31(U43(z0), x1))) A__U61(tt, U31(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatIList(z0), x1)), MARK(U31(isNatIList(z0), x1))) A__U61(tt, U31(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U31(a__U51(mark(z0), z1, z2), x1)), MARK(U31(U51(z0, z1, z2), x1))) A__U61(tt, U31(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U52(mark(z0), z1), x1)), MARK(U31(U52(z0, z1), x1))) A__U61(tt, U31(U53(z0), x1)) -> c26(A__LENGTH(a__U31(a__U53(mark(z0)), x1)), MARK(U31(U53(z0), x1))) A__U61(tt, U31(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U61(mark(z0), z1), x1)), MARK(U31(U61(z0, z1), x1))) A__U61(tt, U31(length(z0), x1)) -> c26(A__LENGTH(a__U31(a__length(mark(z0)), x1)), MARK(U31(length(z0), x1))) A__U61(tt, U31(and(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__and(mark(z0), z1), x1)), MARK(U31(and(z0, z1), x1))) A__U61(tt, U31(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatIListKind(z0), x1)), MARK(U31(isNatIListKind(z0), x1))) A__U61(tt, U31(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatKind(z0), x1)), MARK(U31(isNatKind(z0), x1))) A__U61(tt, U31(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U31(cons(mark(z0), z1), x1)), MARK(U31(cons(z0, z1), x1))) A__U61(tt, U31(0, x1)) -> c26(A__LENGTH(a__U31(0, x1)), MARK(U31(0, x1))) A__U61(tt, U31(tt, x1)) -> c26(A__LENGTH(a__U31(tt, x1)), MARK(U31(tt, x1))) A__U61(tt, U31(s(z0), x1)) -> c26(A__LENGTH(a__U31(s(mark(z0)), x1)), MARK(U31(s(z0), x1))) A__U61(tt, U31(nil, x1)) -> c26(A__LENGTH(a__U31(nil, x1)), MARK(U31(nil, x1))) ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), 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MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> 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MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> c26(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U61(tt, U12(U21(z0, z1))) -> c26(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U61(tt, U12(U22(z0))) -> c26(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U61(tt, U12(isNat(z0))) -> c26(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U61(tt, U12(U31(z0, z1))) -> c26(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U61(tt, U12(U32(z0))) -> c26(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U61(tt, U12(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U61(tt, U12(U42(z0, z1))) -> c26(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U61(tt, U12(U43(z0))) -> c26(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U61(tt, U12(isNatIList(z0))) -> c26(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U61(tt, U12(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U61(tt, U12(U52(z0, z1))) -> c26(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U61(tt, U12(U53(z0))) -> c26(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U61(tt, U12(U61(z0, z1))) -> c26(A__LENGTH(a__U12(a__U61(mark(z0), z1))), MARK(U12(U61(z0, z1)))) A__U61(tt, U12(length(z0))) -> c26(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U61(tt, U12(and(z0, z1))) -> c26(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U61(tt, U12(isNatIListKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U61(tt, U12(isNatKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U61(tt, U12(cons(z0, z1))) -> c26(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U61(tt, U12(0)) -> c26(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U61(tt, U12(tt)) -> c26(A__LENGTH(a__U12(tt)), MARK(U12(tt))) A__U61(tt, U12(s(z0))) -> c26(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U61(tt, U12(nil)) -> c26(A__LENGTH(a__U12(nil)), MARK(U12(nil))) A__U61(tt, U12(x0)) -> c26(MARK(U12(x0))) A__U61(tt, isNatList(cons(z0, z1))) -> c26(A__LENGTH(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(cons(z0, z1)))) A__U61(tt, isNatList(nil)) -> c26(MARK(isNatList(nil))) A__U61(tt, isNatList(z0)) -> c26(MARK(isNatList(z0))) A__U61(tt, U21(zeros, x1)) -> c26(A__LENGTH(a__U21(a__zeros, x1)), MARK(U21(zeros, x1))) A__U61(tt, U21(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1)), MARK(U21(U11(z0, z1), x1))) A__U61(tt, U21(U12(z0), x1)) -> c26(A__LENGTH(a__U21(a__U12(mark(z0)), x1)), MARK(U21(U12(z0), x1))) A__U61(tt, U21(isNatList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatList(z0), x1)), MARK(U21(isNatList(z0), x1))) A__U61(tt, U21(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U21(mark(z0), z1), x1)), MARK(U21(U21(z0, z1), x1))) A__U61(tt, U21(U22(z0), x1)) -> c26(A__LENGTH(a__U21(a__U22(mark(z0)), x1)), MARK(U21(U22(z0), x1))) A__U61(tt, U21(isNat(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNat(z0), x1)), MARK(U21(isNat(z0), x1))) A__U61(tt, U21(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U31(mark(z0), z1), x1)), MARK(U21(U31(z0, z1), x1))) A__U61(tt, U21(U32(z0), x1)) -> c26(A__LENGTH(a__U21(a__U32(mark(z0)), x1)), MARK(U21(U32(z0), x1))) A__U61(tt, U21(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(U21(U41(z0, z1, z2), x1))) A__U61(tt, U21(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U42(mark(z0), z1), x1)), MARK(U21(U42(z0, z1), x1))) A__U61(tt, U21(U43(z0), x1)) -> c26(A__LENGTH(a__U21(a__U43(mark(z0)), x1)), MARK(U21(U43(z0), x1))) A__U61(tt, U21(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIList(z0), x1)), MARK(U21(isNatIList(z0), x1))) A__U61(tt, U21(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U51(mark(z0), z1, z2), x1)), MARK(U21(U51(z0, z1, z2), x1))) A__U61(tt, U21(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U52(mark(z0), z1), x1)), MARK(U21(U52(z0, z1), x1))) A__U61(tt, U21(U53(z0), x1)) -> c26(A__LENGTH(a__U21(a__U53(mark(z0)), x1)), MARK(U21(U53(z0), x1))) A__U61(tt, U21(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U61(mark(z0), z1), x1)), MARK(U21(U61(z0, z1), x1))) A__U61(tt, U21(length(z0), x1)) -> c26(A__LENGTH(a__U21(a__length(mark(z0)), x1)), MARK(U21(length(z0), x1))) A__U61(tt, U21(and(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__and(mark(z0), z1), x1)), MARK(U21(and(z0, z1), x1))) A__U61(tt, U21(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIListKind(z0), x1)), MARK(U21(isNatIListKind(z0), x1))) A__U61(tt, U21(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), x1)), MARK(U21(isNatKind(z0), x1))) A__U61(tt, U21(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U21(cons(mark(z0), z1), x1)), MARK(U21(cons(z0, z1), x1))) A__U61(tt, U21(tt, x1)) -> c26(A__LENGTH(a__U21(tt, x1)), MARK(U21(tt, x1))) A__U61(tt, U21(s(z0), x1)) -> c26(A__LENGTH(a__U21(s(mark(z0)), x1)), MARK(U21(s(z0), x1))) A__U61(tt, U21(x0, z1)) -> c26(MARK(U21(x0, z1))) A__U61(tt, U21(0, x1)) -> c26(A__LENGTH(a__U21(0, x1))) A__U61(tt, U21(nil, x1)) -> c26(A__LENGTH(a__U21(nil, x1))) A__U61(tt, U22(zeros)) -> c26(A__LENGTH(a__U22(a__zeros)), MARK(U22(zeros))) A__U61(tt, U22(U11(z0, z1))) -> c26(A__LENGTH(a__U22(a__U11(mark(z0), z1))), MARK(U22(U11(z0, z1)))) A__U61(tt, U22(U12(z0))) -> c26(A__LENGTH(a__U22(a__U12(mark(z0)))), MARK(U22(U12(z0)))) A__U61(tt, U22(isNatList(z0))) -> c26(A__LENGTH(a__U22(a__isNatList(z0))), MARK(U22(isNatList(z0)))) A__U61(tt, U22(U21(z0, z1))) -> c26(A__LENGTH(a__U22(a__U21(mark(z0), z1))), MARK(U22(U21(z0, z1)))) A__U61(tt, U22(U22(z0))) -> c26(A__LENGTH(a__U22(a__U22(mark(z0)))), MARK(U22(U22(z0)))) A__U61(tt, U22(isNat(z0))) -> c26(A__LENGTH(a__U22(a__isNat(z0))), MARK(U22(isNat(z0)))) A__U61(tt, U22(U31(z0, z1))) -> c26(A__LENGTH(a__U22(a__U31(mark(z0), z1))), MARK(U22(U31(z0, z1)))) A__U61(tt, U22(U32(z0))) -> c26(A__LENGTH(a__U22(a__U32(mark(z0)))), MARK(U22(U32(z0)))) A__U61(tt, U22(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U22(a__U41(mark(z0), z1, z2))), MARK(U22(U41(z0, z1, z2)))) A__U61(tt, U22(U42(z0, z1))) -> c26(A__LENGTH(a__U22(a__U42(mark(z0), z1))), MARK(U22(U42(z0, z1)))) A__U61(tt, U22(U43(z0))) -> c26(A__LENGTH(a__U22(a__U43(mark(z0)))), MARK(U22(U43(z0)))) A__U61(tt, U22(isNatIList(z0))) -> c26(A__LENGTH(a__U22(a__isNatIList(z0))), MARK(U22(isNatIList(z0)))) A__U61(tt, U22(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U22(a__U51(mark(z0), z1, z2))), MARK(U22(U51(z0, z1, z2)))) A__U61(tt, U22(U52(z0, z1))) -> c26(A__LENGTH(a__U22(a__U52(mark(z0), z1))), MARK(U22(U52(z0, z1)))) A__U61(tt, U22(U53(z0))) -> c26(A__LENGTH(a__U22(a__U53(mark(z0)))), MARK(U22(U53(z0)))) A__U61(tt, U22(U61(z0, z1))) -> c26(A__LENGTH(a__U22(a__U61(mark(z0), z1))), MARK(U22(U61(z0, z1)))) A__U61(tt, U22(length(z0))) -> c26(A__LENGTH(a__U22(a__length(mark(z0)))), MARK(U22(length(z0)))) A__U61(tt, U22(and(z0, z1))) -> c26(A__LENGTH(a__U22(a__and(mark(z0), z1))), MARK(U22(and(z0, z1)))) A__U61(tt, U22(isNatIListKind(z0))) -> c26(A__LENGTH(a__U22(a__isNatIListKind(z0))), MARK(U22(isNatIListKind(z0)))) A__U61(tt, U22(isNatKind(z0))) -> c26(A__LENGTH(a__U22(a__isNatKind(z0))), MARK(U22(isNatKind(z0)))) A__U61(tt, U22(cons(z0, z1))) -> c26(A__LENGTH(a__U22(cons(mark(z0), z1))), MARK(U22(cons(z0, z1)))) A__U61(tt, U22(0)) -> c26(A__LENGTH(a__U22(0)), MARK(U22(0))) A__U61(tt, U22(tt)) -> c26(A__LENGTH(a__U22(tt)), MARK(U22(tt))) A__U61(tt, U22(s(z0))) -> c26(A__LENGTH(a__U22(s(mark(z0)))), MARK(U22(s(z0)))) A__U61(tt, U22(nil)) -> c26(A__LENGTH(a__U22(nil)), MARK(U22(nil))) A__U61(tt, U22(x0)) -> c26(MARK(U22(x0))) A__U61(tt, isNat(length(z0))) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), z0)), MARK(isNat(length(z0)))) A__U61(tt, isNat(s(z0))) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), z0)), MARK(isNat(s(z0)))) A__U61(tt, isNat(0)) -> c26(MARK(isNat(0))) A__U61(tt, isNat(z0)) -> c26(MARK(isNat(z0))) A__U61(tt, U31(x0, z1)) -> c26(A__LENGTH(U31(mark(x0), z1)), MARK(U31(x0, z1))) A__U61(tt, U31(zeros, x1)) -> c26(A__LENGTH(a__U31(a__zeros, x1)), MARK(U31(zeros, x1))) A__U61(tt, U31(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U11(mark(z0), z1), x1)), MARK(U31(U11(z0, z1), x1))) A__U61(tt, U31(U12(z0), x1)) -> c26(A__LENGTH(a__U31(a__U12(mark(z0)), x1)), MARK(U31(U12(z0), x1))) A__U61(tt, U31(isNatList(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatList(z0), x1)), MARK(U31(isNatList(z0), x1))) A__U61(tt, U31(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U21(mark(z0), z1), x1)), MARK(U31(U21(z0, z1), x1))) A__U61(tt, U31(U22(z0), x1)) -> c26(A__LENGTH(a__U31(a__U22(mark(z0)), x1)), MARK(U31(U22(z0), x1))) A__U61(tt, U31(isNat(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNat(z0), x1)), MARK(U31(isNat(z0), x1))) A__U61(tt, U31(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U31(mark(z0), z1), x1)), MARK(U31(U31(z0, z1), x1))) A__U61(tt, U31(U32(z0), x1)) -> c26(A__LENGTH(a__U31(a__U32(mark(z0)), x1)), MARK(U31(U32(z0), x1))) A__U61(tt, U31(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(U31(U41(z0, z1, z2), x1))) A__U61(tt, U31(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U42(mark(z0), z1), x1)), MARK(U31(U42(z0, z1), x1))) A__U61(tt, U31(U43(z0), x1)) -> c26(A__LENGTH(a__U31(a__U43(mark(z0)), x1)), MARK(U31(U43(z0), x1))) A__U61(tt, U31(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatIList(z0), x1)), MARK(U31(isNatIList(z0), x1))) A__U61(tt, U31(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U31(a__U51(mark(z0), z1, z2), x1)), MARK(U31(U51(z0, z1, z2), x1))) A__U61(tt, U31(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U52(mark(z0), z1), x1)), MARK(U31(U52(z0, z1), x1))) A__U61(tt, U31(U53(z0), x1)) -> c26(A__LENGTH(a__U31(a__U53(mark(z0)), x1)), MARK(U31(U53(z0), x1))) A__U61(tt, U31(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U61(mark(z0), z1), x1)), MARK(U31(U61(z0, z1), x1))) A__U61(tt, U31(length(z0), x1)) -> c26(A__LENGTH(a__U31(a__length(mark(z0)), x1)), MARK(U31(length(z0), x1))) A__U61(tt, U31(and(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__and(mark(z0), z1), x1)), MARK(U31(and(z0, z1), x1))) A__U61(tt, U31(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatIListKind(z0), x1)), MARK(U31(isNatIListKind(z0), x1))) A__U61(tt, U31(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatKind(z0), x1)), MARK(U31(isNatKind(z0), x1))) A__U61(tt, U31(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U31(cons(mark(z0), z1), x1)), MARK(U31(cons(z0, z1), x1))) A__U61(tt, U31(0, x1)) -> c26(A__LENGTH(a__U31(0, x1)), MARK(U31(0, x1))) A__U61(tt, U31(tt, x1)) -> c26(A__LENGTH(a__U31(tt, x1)), MARK(U31(tt, x1))) A__U61(tt, U31(s(z0), x1)) -> c26(A__LENGTH(a__U31(s(mark(z0)), x1)), MARK(U31(s(z0), x1))) A__U61(tt, U31(nil, x1)) -> c26(A__LENGTH(a__U31(nil, x1)), MARK(U31(nil, x1))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), 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c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, 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MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> c26(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U61(tt, U12(U21(z0, z1))) -> c26(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U61(tt, U12(U22(z0))) -> c26(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U61(tt, U12(isNat(z0))) -> c26(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U61(tt, U12(U31(z0, z1))) -> c26(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U61(tt, U12(U32(z0))) -> c26(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U61(tt, U12(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U61(tt, U12(U42(z0, z1))) -> c26(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U61(tt, U12(U43(z0))) -> c26(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U61(tt, U12(isNatIList(z0))) -> c26(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U61(tt, U12(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U61(tt, U12(U52(z0, z1))) -> c26(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U61(tt, U12(U53(z0))) -> c26(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U61(tt, U12(U61(z0, z1))) -> c26(A__LENGTH(a__U12(a__U61(mark(z0), z1))), MARK(U12(U61(z0, z1)))) A__U61(tt, U12(length(z0))) -> c26(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U61(tt, U12(and(z0, z1))) -> c26(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U61(tt, U12(isNatIListKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U61(tt, U12(isNatKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U61(tt, U12(cons(z0, z1))) -> c26(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U61(tt, U12(0)) -> c26(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U61(tt, U12(tt)) -> c26(A__LENGTH(a__U12(tt)), MARK(U12(tt))) A__U61(tt, U12(s(z0))) -> c26(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U61(tt, U12(nil)) -> c26(A__LENGTH(a__U12(nil)), MARK(U12(nil))) A__U61(tt, U12(x0)) -> c26(MARK(U12(x0))) A__U61(tt, isNatList(cons(z0, z1))) -> c26(A__LENGTH(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(cons(z0, z1)))) A__U61(tt, isNatList(nil)) -> c26(MARK(isNatList(nil))) A__U61(tt, isNatList(z0)) -> c26(MARK(isNatList(z0))) A__U61(tt, U21(zeros, x1)) -> c26(A__LENGTH(a__U21(a__zeros, x1)), MARK(U21(zeros, x1))) A__U61(tt, U21(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1)), MARK(U21(U11(z0, z1), x1))) A__U61(tt, U21(U12(z0), x1)) -> c26(A__LENGTH(a__U21(a__U12(mark(z0)), x1)), MARK(U21(U12(z0), x1))) A__U61(tt, U21(isNatList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatList(z0), x1)), MARK(U21(isNatList(z0), x1))) A__U61(tt, U21(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U21(mark(z0), z1), x1)), MARK(U21(U21(z0, z1), x1))) A__U61(tt, U21(U22(z0), x1)) -> c26(A__LENGTH(a__U21(a__U22(mark(z0)), x1)), MARK(U21(U22(z0), x1))) A__U61(tt, U21(isNat(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNat(z0), x1)), MARK(U21(isNat(z0), x1))) A__U61(tt, U21(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U31(mark(z0), z1), x1)), MARK(U21(U31(z0, z1), x1))) A__U61(tt, U21(U32(z0), x1)) -> c26(A__LENGTH(a__U21(a__U32(mark(z0)), x1)), MARK(U21(U32(z0), x1))) A__U61(tt, U21(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(U21(U41(z0, z1, z2), x1))) A__U61(tt, U21(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U42(mark(z0), z1), x1)), MARK(U21(U42(z0, z1), x1))) A__U61(tt, U21(U43(z0), x1)) -> c26(A__LENGTH(a__U21(a__U43(mark(z0)), x1)), MARK(U21(U43(z0), x1))) A__U61(tt, U21(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIList(z0), x1)), MARK(U21(isNatIList(z0), x1))) A__U61(tt, U21(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U51(mark(z0), z1, z2), x1)), MARK(U21(U51(z0, z1, z2), x1))) A__U61(tt, U21(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U52(mark(z0), z1), x1)), MARK(U21(U52(z0, z1), x1))) A__U61(tt, U21(U53(z0), x1)) -> c26(A__LENGTH(a__U21(a__U53(mark(z0)), x1)), MARK(U21(U53(z0), x1))) A__U61(tt, U21(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U61(mark(z0), z1), x1)), MARK(U21(U61(z0, z1), x1))) A__U61(tt, U21(length(z0), x1)) -> c26(A__LENGTH(a__U21(a__length(mark(z0)), x1)), MARK(U21(length(z0), x1))) A__U61(tt, U21(and(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__and(mark(z0), z1), x1)), MARK(U21(and(z0, z1), x1))) A__U61(tt, U21(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIListKind(z0), x1)), MARK(U21(isNatIListKind(z0), x1))) A__U61(tt, U21(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), x1)), MARK(U21(isNatKind(z0), x1))) A__U61(tt, U21(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U21(cons(mark(z0), z1), x1)), MARK(U21(cons(z0, z1), x1))) A__U61(tt, U21(tt, x1)) -> c26(A__LENGTH(a__U21(tt, x1)), MARK(U21(tt, x1))) A__U61(tt, U21(s(z0), x1)) -> c26(A__LENGTH(a__U21(s(mark(z0)), x1)), MARK(U21(s(z0), x1))) A__U61(tt, U21(x0, z1)) -> c26(MARK(U21(x0, z1))) A__U61(tt, U21(0, x1)) -> c26(A__LENGTH(a__U21(0, x1))) A__U61(tt, U21(nil, x1)) -> c26(A__LENGTH(a__U21(nil, x1))) A__U61(tt, U22(zeros)) -> c26(A__LENGTH(a__U22(a__zeros)), MARK(U22(zeros))) A__U61(tt, U22(U11(z0, z1))) -> c26(A__LENGTH(a__U22(a__U11(mark(z0), z1))), MARK(U22(U11(z0, z1)))) A__U61(tt, U22(U12(z0))) -> c26(A__LENGTH(a__U22(a__U12(mark(z0)))), MARK(U22(U12(z0)))) A__U61(tt, U22(isNatList(z0))) -> c26(A__LENGTH(a__U22(a__isNatList(z0))), MARK(U22(isNatList(z0)))) A__U61(tt, U22(U21(z0, z1))) -> c26(A__LENGTH(a__U22(a__U21(mark(z0), z1))), MARK(U22(U21(z0, z1)))) A__U61(tt, U22(U22(z0))) -> c26(A__LENGTH(a__U22(a__U22(mark(z0)))), MARK(U22(U22(z0)))) A__U61(tt, U22(isNat(z0))) -> c26(A__LENGTH(a__U22(a__isNat(z0))), MARK(U22(isNat(z0)))) A__U61(tt, U22(U31(z0, z1))) -> c26(A__LENGTH(a__U22(a__U31(mark(z0), z1))), MARK(U22(U31(z0, z1)))) A__U61(tt, U22(U32(z0))) -> c26(A__LENGTH(a__U22(a__U32(mark(z0)))), MARK(U22(U32(z0)))) A__U61(tt, U22(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U22(a__U41(mark(z0), z1, z2))), MARK(U22(U41(z0, z1, z2)))) A__U61(tt, U22(U42(z0, z1))) -> c26(A__LENGTH(a__U22(a__U42(mark(z0), z1))), MARK(U22(U42(z0, z1)))) A__U61(tt, U22(U43(z0))) -> c26(A__LENGTH(a__U22(a__U43(mark(z0)))), MARK(U22(U43(z0)))) A__U61(tt, U22(isNatIList(z0))) -> c26(A__LENGTH(a__U22(a__isNatIList(z0))), MARK(U22(isNatIList(z0)))) A__U61(tt, U22(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U22(a__U51(mark(z0), z1, z2))), MARK(U22(U51(z0, z1, z2)))) A__U61(tt, U22(U52(z0, z1))) -> c26(A__LENGTH(a__U22(a__U52(mark(z0), z1))), MARK(U22(U52(z0, z1)))) A__U61(tt, U22(U53(z0))) -> c26(A__LENGTH(a__U22(a__U53(mark(z0)))), MARK(U22(U53(z0)))) A__U61(tt, U22(U61(z0, z1))) -> c26(A__LENGTH(a__U22(a__U61(mark(z0), z1))), MARK(U22(U61(z0, z1)))) A__U61(tt, U22(length(z0))) -> c26(A__LENGTH(a__U22(a__length(mark(z0)))), MARK(U22(length(z0)))) A__U61(tt, U22(and(z0, z1))) -> c26(A__LENGTH(a__U22(a__and(mark(z0), z1))), MARK(U22(and(z0, z1)))) A__U61(tt, U22(isNatIListKind(z0))) -> c26(A__LENGTH(a__U22(a__isNatIListKind(z0))), MARK(U22(isNatIListKind(z0)))) A__U61(tt, U22(isNatKind(z0))) -> c26(A__LENGTH(a__U22(a__isNatKind(z0))), MARK(U22(isNatKind(z0)))) A__U61(tt, U22(cons(z0, z1))) -> c26(A__LENGTH(a__U22(cons(mark(z0), z1))), MARK(U22(cons(z0, z1)))) A__U61(tt, U22(0)) -> c26(A__LENGTH(a__U22(0)), MARK(U22(0))) A__U61(tt, U22(tt)) -> c26(A__LENGTH(a__U22(tt)), MARK(U22(tt))) A__U61(tt, U22(s(z0))) -> c26(A__LENGTH(a__U22(s(mark(z0)))), MARK(U22(s(z0)))) A__U61(tt, U22(nil)) -> c26(A__LENGTH(a__U22(nil)), MARK(U22(nil))) A__U61(tt, U22(x0)) -> c26(MARK(U22(x0))) A__U61(tt, isNat(length(z0))) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), z0)), MARK(isNat(length(z0)))) A__U61(tt, isNat(s(z0))) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), z0)), MARK(isNat(s(z0)))) A__U61(tt, isNat(0)) -> c26(MARK(isNat(0))) A__U61(tt, isNat(z0)) -> c26(MARK(isNat(z0))) A__U61(tt, U31(x0, z1)) -> c26(A__LENGTH(U31(mark(x0), z1)), MARK(U31(x0, z1))) A__U61(tt, U31(zeros, x1)) -> c26(A__LENGTH(a__U31(a__zeros, x1)), MARK(U31(zeros, x1))) A__U61(tt, U31(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U11(mark(z0), z1), x1)), MARK(U31(U11(z0, z1), x1))) A__U61(tt, U31(U12(z0), x1)) -> c26(A__LENGTH(a__U31(a__U12(mark(z0)), x1)), MARK(U31(U12(z0), x1))) A__U61(tt, U31(isNatList(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatList(z0), x1)), MARK(U31(isNatList(z0), x1))) A__U61(tt, U31(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U21(mark(z0), z1), x1)), MARK(U31(U21(z0, z1), x1))) A__U61(tt, U31(U22(z0), x1)) -> c26(A__LENGTH(a__U31(a__U22(mark(z0)), x1)), MARK(U31(U22(z0), x1))) A__U61(tt, U31(isNat(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNat(z0), x1)), MARK(U31(isNat(z0), x1))) A__U61(tt, U31(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U31(mark(z0), z1), x1)), MARK(U31(U31(z0, z1), x1))) A__U61(tt, U31(U32(z0), x1)) -> c26(A__LENGTH(a__U31(a__U32(mark(z0)), x1)), MARK(U31(U32(z0), x1))) A__U61(tt, U31(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(U31(U41(z0, z1, z2), x1))) A__U61(tt, U31(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U42(mark(z0), z1), x1)), MARK(U31(U42(z0, z1), x1))) A__U61(tt, U31(U43(z0), x1)) -> c26(A__LENGTH(a__U31(a__U43(mark(z0)), x1)), MARK(U31(U43(z0), x1))) A__U61(tt, U31(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatIList(z0), x1)), MARK(U31(isNatIList(z0), x1))) A__U61(tt, U31(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U31(a__U51(mark(z0), z1, z2), x1)), MARK(U31(U51(z0, z1, z2), x1))) A__U61(tt, U31(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U52(mark(z0), z1), x1)), MARK(U31(U52(z0, z1), x1))) A__U61(tt, U31(U53(z0), x1)) -> c26(A__LENGTH(a__U31(a__U53(mark(z0)), x1)), MARK(U31(U53(z0), x1))) A__U61(tt, U31(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U61(mark(z0), z1), x1)), MARK(U31(U61(z0, z1), x1))) A__U61(tt, U31(length(z0), x1)) -> c26(A__LENGTH(a__U31(a__length(mark(z0)), x1)), MARK(U31(length(z0), x1))) A__U61(tt, U31(and(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__and(mark(z0), z1), x1)), MARK(U31(and(z0, z1), x1))) A__U61(tt, U31(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatIListKind(z0), x1)), MARK(U31(isNatIListKind(z0), x1))) A__U61(tt, U31(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatKind(z0), x1)), MARK(U31(isNatKind(z0), x1))) A__U61(tt, U31(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U31(cons(mark(z0), z1), x1)), MARK(U31(cons(z0, z1), x1))) A__U61(tt, U31(0, x1)) -> c26(A__LENGTH(a__U31(0, x1)), MARK(U31(0, x1))) A__U61(tt, U31(tt, x1)) -> c26(A__LENGTH(a__U31(tt, x1)), MARK(U31(tt, x1))) A__U61(tt, U31(s(z0), x1)) -> c26(A__LENGTH(a__U31(s(mark(z0)), x1)), MARK(U31(s(z0), x1))) A__U61(tt, U31(nil, x1)) -> c26(A__LENGTH(a__U31(nil, x1)), MARK(U31(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_1, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c14_2, c20_2 ---------------------------------------- (173) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> c26(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U61(tt, U12(U21(z0, z1))) -> c26(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U61(tt, U12(U22(z0))) -> c26(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U61(tt, U12(isNat(z0))) -> c26(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U61(tt, U12(U31(z0, z1))) -> c26(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U61(tt, U12(U32(z0))) -> c26(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U61(tt, U12(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U61(tt, U12(U42(z0, z1))) -> c26(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U61(tt, U12(U43(z0))) -> c26(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U61(tt, U12(isNatIList(z0))) -> c26(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U61(tt, U12(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U61(tt, U12(U52(z0, z1))) -> c26(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U61(tt, U12(U53(z0))) -> c26(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U61(tt, U12(U61(z0, z1))) -> c26(A__LENGTH(a__U12(a__U61(mark(z0), z1))), MARK(U12(U61(z0, z1)))) A__U61(tt, U12(length(z0))) -> c26(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U61(tt, U12(and(z0, z1))) -> c26(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U61(tt, U12(isNatIListKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U61(tt, U12(isNatKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U61(tt, U12(cons(z0, z1))) -> c26(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U61(tt, U12(0)) -> c26(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U61(tt, U12(tt)) -> c26(A__LENGTH(a__U12(tt)), MARK(U12(tt))) A__U61(tt, U12(s(z0))) -> c26(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U61(tt, U12(nil)) -> c26(A__LENGTH(a__U12(nil)), MARK(U12(nil))) A__U61(tt, U12(x0)) -> c26(MARK(U12(x0))) A__U61(tt, isNatList(cons(z0, z1))) -> c26(A__LENGTH(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(cons(z0, z1)))) A__U61(tt, isNatList(nil)) -> c26(MARK(isNatList(nil))) A__U61(tt, isNatList(z0)) -> c26(MARK(isNatList(z0))) A__U61(tt, U21(zeros, x1)) -> c26(A__LENGTH(a__U21(a__zeros, x1)), MARK(U21(zeros, x1))) A__U61(tt, U21(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1)), MARK(U21(U11(z0, z1), x1))) A__U61(tt, U21(U12(z0), x1)) -> c26(A__LENGTH(a__U21(a__U12(mark(z0)), x1)), MARK(U21(U12(z0), x1))) A__U61(tt, U21(isNatList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatList(z0), x1)), MARK(U21(isNatList(z0), x1))) A__U61(tt, U21(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U21(mark(z0), z1), x1)), MARK(U21(U21(z0, z1), x1))) A__U61(tt, U21(U22(z0), x1)) -> c26(A__LENGTH(a__U21(a__U22(mark(z0)), x1)), MARK(U21(U22(z0), x1))) A__U61(tt, U21(isNat(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNat(z0), x1)), MARK(U21(isNat(z0), x1))) A__U61(tt, U21(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U31(mark(z0), z1), x1)), MARK(U21(U31(z0, z1), x1))) A__U61(tt, U21(U32(z0), x1)) -> c26(A__LENGTH(a__U21(a__U32(mark(z0)), x1)), MARK(U21(U32(z0), x1))) A__U61(tt, U21(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(U21(U41(z0, z1, z2), x1))) A__U61(tt, U21(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U42(mark(z0), z1), x1)), MARK(U21(U42(z0, z1), x1))) A__U61(tt, U21(U43(z0), x1)) -> c26(A__LENGTH(a__U21(a__U43(mark(z0)), x1)), MARK(U21(U43(z0), x1))) A__U61(tt, U21(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIList(z0), x1)), MARK(U21(isNatIList(z0), x1))) A__U61(tt, U21(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U51(mark(z0), z1, z2), x1)), MARK(U21(U51(z0, z1, z2), x1))) A__U61(tt, U21(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U52(mark(z0), z1), x1)), MARK(U21(U52(z0, z1), x1))) A__U61(tt, U21(U53(z0), x1)) -> c26(A__LENGTH(a__U21(a__U53(mark(z0)), x1)), MARK(U21(U53(z0), x1))) A__U61(tt, U21(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U61(mark(z0), z1), x1)), MARK(U21(U61(z0, z1), x1))) A__U61(tt, U21(length(z0), x1)) -> c26(A__LENGTH(a__U21(a__length(mark(z0)), x1)), MARK(U21(length(z0), x1))) A__U61(tt, U21(and(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__and(mark(z0), z1), x1)), MARK(U21(and(z0, z1), x1))) A__U61(tt, U21(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIListKind(z0), x1)), MARK(U21(isNatIListKind(z0), x1))) A__U61(tt, U21(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), x1)), MARK(U21(isNatKind(z0), x1))) A__U61(tt, U21(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U21(cons(mark(z0), z1), x1)), MARK(U21(cons(z0, z1), x1))) A__U61(tt, U21(tt, x1)) -> c26(A__LENGTH(a__U21(tt, x1)), MARK(U21(tt, x1))) A__U61(tt, U21(s(z0), x1)) -> c26(A__LENGTH(a__U21(s(mark(z0)), x1)), MARK(U21(s(z0), x1))) A__U61(tt, U21(x0, z1)) -> c26(MARK(U21(x0, z1))) A__U61(tt, U21(0, x1)) -> c26(A__LENGTH(a__U21(0, x1))) A__U61(tt, U21(nil, x1)) -> c26(A__LENGTH(a__U21(nil, x1))) A__U61(tt, U22(zeros)) -> c26(A__LENGTH(a__U22(a__zeros)), MARK(U22(zeros))) A__U61(tt, U22(U11(z0, z1))) -> c26(A__LENGTH(a__U22(a__U11(mark(z0), z1))), MARK(U22(U11(z0, z1)))) A__U61(tt, U22(U12(z0))) -> c26(A__LENGTH(a__U22(a__U12(mark(z0)))), MARK(U22(U12(z0)))) A__U61(tt, U22(isNatList(z0))) -> c26(A__LENGTH(a__U22(a__isNatList(z0))), MARK(U22(isNatList(z0)))) A__U61(tt, U22(U21(z0, z1))) -> c26(A__LENGTH(a__U22(a__U21(mark(z0), z1))), MARK(U22(U21(z0, z1)))) A__U61(tt, U22(U22(z0))) -> c26(A__LENGTH(a__U22(a__U22(mark(z0)))), MARK(U22(U22(z0)))) A__U61(tt, U22(isNat(z0))) -> c26(A__LENGTH(a__U22(a__isNat(z0))), MARK(U22(isNat(z0)))) A__U61(tt, U22(U31(z0, z1))) -> c26(A__LENGTH(a__U22(a__U31(mark(z0), z1))), MARK(U22(U31(z0, z1)))) A__U61(tt, U22(U32(z0))) -> c26(A__LENGTH(a__U22(a__U32(mark(z0)))), MARK(U22(U32(z0)))) A__U61(tt, U22(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U22(a__U41(mark(z0), z1, z2))), MARK(U22(U41(z0, z1, z2)))) A__U61(tt, U22(U42(z0, z1))) -> c26(A__LENGTH(a__U22(a__U42(mark(z0), z1))), MARK(U22(U42(z0, z1)))) A__U61(tt, U22(U43(z0))) -> c26(A__LENGTH(a__U22(a__U43(mark(z0)))), MARK(U22(U43(z0)))) A__U61(tt, U22(isNatIList(z0))) -> c26(A__LENGTH(a__U22(a__isNatIList(z0))), MARK(U22(isNatIList(z0)))) A__U61(tt, U22(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U22(a__U51(mark(z0), z1, z2))), MARK(U22(U51(z0, z1, z2)))) A__U61(tt, U22(U52(z0, z1))) -> c26(A__LENGTH(a__U22(a__U52(mark(z0), z1))), MARK(U22(U52(z0, z1)))) A__U61(tt, U22(U53(z0))) -> c26(A__LENGTH(a__U22(a__U53(mark(z0)))), MARK(U22(U53(z0)))) A__U61(tt, U22(U61(z0, z1))) -> c26(A__LENGTH(a__U22(a__U61(mark(z0), z1))), MARK(U22(U61(z0, z1)))) A__U61(tt, U22(length(z0))) -> c26(A__LENGTH(a__U22(a__length(mark(z0)))), MARK(U22(length(z0)))) A__U61(tt, U22(and(z0, z1))) -> c26(A__LENGTH(a__U22(a__and(mark(z0), z1))), MARK(U22(and(z0, z1)))) A__U61(tt, U22(isNatIListKind(z0))) -> c26(A__LENGTH(a__U22(a__isNatIListKind(z0))), MARK(U22(isNatIListKind(z0)))) A__U61(tt, U22(isNatKind(z0))) -> c26(A__LENGTH(a__U22(a__isNatKind(z0))), MARK(U22(isNatKind(z0)))) A__U61(tt, U22(cons(z0, z1))) -> c26(A__LENGTH(a__U22(cons(mark(z0), z1))), MARK(U22(cons(z0, z1)))) A__U61(tt, U22(0)) -> c26(A__LENGTH(a__U22(0)), MARK(U22(0))) A__U61(tt, U22(tt)) -> c26(A__LENGTH(a__U22(tt)), MARK(U22(tt))) A__U61(tt, U22(s(z0))) -> c26(A__LENGTH(a__U22(s(mark(z0)))), MARK(U22(s(z0)))) A__U61(tt, U22(nil)) -> c26(A__LENGTH(a__U22(nil)), MARK(U22(nil))) A__U61(tt, U22(x0)) -> c26(MARK(U22(x0))) A__U61(tt, isNat(length(z0))) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), z0)), MARK(isNat(length(z0)))) A__U61(tt, isNat(s(z0))) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), z0)), MARK(isNat(s(z0)))) A__U61(tt, isNat(0)) -> c26(MARK(isNat(0))) A__U61(tt, isNat(z0)) -> c26(MARK(isNat(z0))) A__U61(tt, U31(zeros, x1)) -> c26(A__LENGTH(a__U31(a__zeros, x1)), MARK(U31(zeros, x1))) A__U61(tt, U31(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U11(mark(z0), z1), x1)), MARK(U31(U11(z0, z1), x1))) A__U61(tt, U31(U12(z0), x1)) -> c26(A__LENGTH(a__U31(a__U12(mark(z0)), x1)), MARK(U31(U12(z0), x1))) A__U61(tt, U31(isNatList(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatList(z0), x1)), MARK(U31(isNatList(z0), x1))) A__U61(tt, U31(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U21(mark(z0), z1), x1)), MARK(U31(U21(z0, z1), x1))) A__U61(tt, U31(U22(z0), x1)) -> c26(A__LENGTH(a__U31(a__U22(mark(z0)), x1)), MARK(U31(U22(z0), x1))) A__U61(tt, U31(isNat(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNat(z0), x1)), MARK(U31(isNat(z0), x1))) A__U61(tt, U31(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U31(mark(z0), z1), x1)), MARK(U31(U31(z0, z1), x1))) A__U61(tt, U31(U32(z0), x1)) -> c26(A__LENGTH(a__U31(a__U32(mark(z0)), x1)), MARK(U31(U32(z0), x1))) A__U61(tt, U31(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(U31(U41(z0, z1, z2), x1))) A__U61(tt, U31(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U42(mark(z0), z1), x1)), MARK(U31(U42(z0, z1), x1))) A__U61(tt, U31(U43(z0), x1)) -> c26(A__LENGTH(a__U31(a__U43(mark(z0)), x1)), MARK(U31(U43(z0), x1))) A__U61(tt, U31(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatIList(z0), x1)), MARK(U31(isNatIList(z0), x1))) A__U61(tt, U31(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U31(a__U51(mark(z0), z1, z2), x1)), MARK(U31(U51(z0, z1, z2), x1))) A__U61(tt, U31(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U52(mark(z0), z1), x1)), MARK(U31(U52(z0, z1), x1))) A__U61(tt, U31(U53(z0), x1)) -> c26(A__LENGTH(a__U31(a__U53(mark(z0)), x1)), MARK(U31(U53(z0), x1))) A__U61(tt, U31(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U61(mark(z0), z1), x1)), MARK(U31(U61(z0, z1), x1))) A__U61(tt, U31(length(z0), x1)) -> c26(A__LENGTH(a__U31(a__length(mark(z0)), x1)), MARK(U31(length(z0), x1))) A__U61(tt, U31(and(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__and(mark(z0), z1), x1)), MARK(U31(and(z0, z1), x1))) A__U61(tt, U31(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatIListKind(z0), x1)), MARK(U31(isNatIListKind(z0), x1))) A__U61(tt, U31(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatKind(z0), x1)), MARK(U31(isNatKind(z0), x1))) A__U61(tt, U31(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U31(cons(mark(z0), z1), x1)), MARK(U31(cons(z0, z1), x1))) A__U61(tt, U31(tt, x1)) -> c26(A__LENGTH(a__U31(tt, x1)), MARK(U31(tt, x1))) A__U61(tt, U31(s(z0), x1)) -> c26(A__LENGTH(a__U31(s(mark(z0)), x1)), MARK(U31(s(z0), x1))) A__U61(tt, U31(x0, z1)) -> c26(MARK(U31(x0, z1))) A__U61(tt, U31(0, x1)) -> c26(A__LENGTH(a__U31(0, x1))) A__U61(tt, U31(nil, x1)) -> c26(A__LENGTH(a__U31(nil, x1))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> c26(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U61(tt, U12(U21(z0, z1))) -> c26(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U61(tt, U12(U22(z0))) -> c26(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U61(tt, U12(isNat(z0))) -> c26(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U61(tt, U12(U31(z0, z1))) -> c26(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U61(tt, U12(U32(z0))) -> c26(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U61(tt, U12(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U61(tt, U12(U42(z0, z1))) -> c26(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U61(tt, U12(U43(z0))) -> c26(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U61(tt, U12(isNatIList(z0))) -> c26(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U61(tt, U12(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U61(tt, U12(U52(z0, z1))) -> c26(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U61(tt, U12(U53(z0))) -> c26(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U61(tt, U12(U61(z0, z1))) -> c26(A__LENGTH(a__U12(a__U61(mark(z0), z1))), MARK(U12(U61(z0, z1)))) A__U61(tt, U12(length(z0))) -> c26(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U61(tt, U12(and(z0, z1))) -> c26(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U61(tt, U12(isNatIListKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U61(tt, U12(isNatKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U61(tt, U12(cons(z0, z1))) -> c26(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U61(tt, U12(0)) -> c26(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U61(tt, U12(tt)) -> c26(A__LENGTH(a__U12(tt)), MARK(U12(tt))) A__U61(tt, U12(s(z0))) -> c26(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U61(tt, U12(nil)) -> c26(A__LENGTH(a__U12(nil)), MARK(U12(nil))) A__U61(tt, U12(x0)) -> c26(MARK(U12(x0))) A__U61(tt, isNatList(cons(z0, z1))) -> c26(A__LENGTH(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(cons(z0, z1)))) A__U61(tt, isNatList(nil)) -> c26(MARK(isNatList(nil))) A__U61(tt, isNatList(z0)) -> c26(MARK(isNatList(z0))) A__U61(tt, U21(zeros, x1)) -> c26(A__LENGTH(a__U21(a__zeros, x1)), MARK(U21(zeros, x1))) A__U61(tt, U21(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1)), MARK(U21(U11(z0, z1), x1))) A__U61(tt, U21(U12(z0), x1)) -> c26(A__LENGTH(a__U21(a__U12(mark(z0)), x1)), MARK(U21(U12(z0), x1))) A__U61(tt, U21(isNatList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatList(z0), x1)), MARK(U21(isNatList(z0), x1))) A__U61(tt, U21(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U21(mark(z0), z1), x1)), MARK(U21(U21(z0, z1), x1))) A__U61(tt, U21(U22(z0), x1)) -> c26(A__LENGTH(a__U21(a__U22(mark(z0)), x1)), MARK(U21(U22(z0), x1))) A__U61(tt, U21(isNat(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNat(z0), x1)), MARK(U21(isNat(z0), x1))) A__U61(tt, U21(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U31(mark(z0), z1), x1)), MARK(U21(U31(z0, z1), x1))) A__U61(tt, U21(U32(z0), x1)) -> c26(A__LENGTH(a__U21(a__U32(mark(z0)), x1)), MARK(U21(U32(z0), x1))) A__U61(tt, U21(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(U21(U41(z0, z1, z2), x1))) A__U61(tt, U21(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U42(mark(z0), z1), x1)), MARK(U21(U42(z0, z1), x1))) A__U61(tt, U21(U43(z0), x1)) -> c26(A__LENGTH(a__U21(a__U43(mark(z0)), x1)), MARK(U21(U43(z0), x1))) A__U61(tt, U21(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIList(z0), x1)), MARK(U21(isNatIList(z0), x1))) A__U61(tt, U21(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U51(mark(z0), z1, z2), x1)), MARK(U21(U51(z0, z1, z2), x1))) A__U61(tt, U21(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U52(mark(z0), z1), x1)), MARK(U21(U52(z0, z1), x1))) A__U61(tt, U21(U53(z0), x1)) -> c26(A__LENGTH(a__U21(a__U53(mark(z0)), x1)), MARK(U21(U53(z0), x1))) A__U61(tt, U21(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U61(mark(z0), z1), x1)), MARK(U21(U61(z0, z1), x1))) A__U61(tt, U21(length(z0), x1)) -> c26(A__LENGTH(a__U21(a__length(mark(z0)), x1)), MARK(U21(length(z0), x1))) A__U61(tt, U21(and(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__and(mark(z0), z1), x1)), MARK(U21(and(z0, z1), x1))) A__U61(tt, U21(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIListKind(z0), x1)), MARK(U21(isNatIListKind(z0), x1))) A__U61(tt, U21(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), x1)), MARK(U21(isNatKind(z0), x1))) A__U61(tt, U21(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U21(cons(mark(z0), z1), x1)), MARK(U21(cons(z0, z1), x1))) A__U61(tt, U21(tt, x1)) -> c26(A__LENGTH(a__U21(tt, x1)), MARK(U21(tt, x1))) A__U61(tt, U21(s(z0), x1)) -> c26(A__LENGTH(a__U21(s(mark(z0)), x1)), MARK(U21(s(z0), x1))) A__U61(tt, U21(x0, z1)) -> c26(MARK(U21(x0, z1))) A__U61(tt, U21(0, x1)) -> c26(A__LENGTH(a__U21(0, x1))) A__U61(tt, U21(nil, x1)) -> c26(A__LENGTH(a__U21(nil, x1))) A__U61(tt, U22(zeros)) -> c26(A__LENGTH(a__U22(a__zeros)), MARK(U22(zeros))) A__U61(tt, U22(U11(z0, z1))) -> c26(A__LENGTH(a__U22(a__U11(mark(z0), z1))), MARK(U22(U11(z0, z1)))) A__U61(tt, U22(U12(z0))) -> c26(A__LENGTH(a__U22(a__U12(mark(z0)))), MARK(U22(U12(z0)))) A__U61(tt, U22(isNatList(z0))) -> c26(A__LENGTH(a__U22(a__isNatList(z0))), MARK(U22(isNatList(z0)))) A__U61(tt, U22(U21(z0, z1))) -> c26(A__LENGTH(a__U22(a__U21(mark(z0), z1))), MARK(U22(U21(z0, z1)))) A__U61(tt, U22(U22(z0))) -> c26(A__LENGTH(a__U22(a__U22(mark(z0)))), MARK(U22(U22(z0)))) A__U61(tt, U22(isNat(z0))) -> c26(A__LENGTH(a__U22(a__isNat(z0))), MARK(U22(isNat(z0)))) A__U61(tt, U22(U31(z0, z1))) -> c26(A__LENGTH(a__U22(a__U31(mark(z0), z1))), MARK(U22(U31(z0, z1)))) A__U61(tt, U22(U32(z0))) -> c26(A__LENGTH(a__U22(a__U32(mark(z0)))), MARK(U22(U32(z0)))) A__U61(tt, U22(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U22(a__U41(mark(z0), z1, z2))), MARK(U22(U41(z0, z1, z2)))) A__U61(tt, U22(U42(z0, z1))) -> c26(A__LENGTH(a__U22(a__U42(mark(z0), z1))), MARK(U22(U42(z0, z1)))) A__U61(tt, U22(U43(z0))) -> c26(A__LENGTH(a__U22(a__U43(mark(z0)))), MARK(U22(U43(z0)))) A__U61(tt, U22(isNatIList(z0))) -> c26(A__LENGTH(a__U22(a__isNatIList(z0))), MARK(U22(isNatIList(z0)))) A__U61(tt, U22(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U22(a__U51(mark(z0), z1, z2))), MARK(U22(U51(z0, z1, z2)))) A__U61(tt, U22(U52(z0, z1))) -> c26(A__LENGTH(a__U22(a__U52(mark(z0), z1))), MARK(U22(U52(z0, z1)))) A__U61(tt, U22(U53(z0))) -> c26(A__LENGTH(a__U22(a__U53(mark(z0)))), MARK(U22(U53(z0)))) A__U61(tt, U22(U61(z0, z1))) -> c26(A__LENGTH(a__U22(a__U61(mark(z0), z1))), MARK(U22(U61(z0, z1)))) A__U61(tt, U22(length(z0))) -> c26(A__LENGTH(a__U22(a__length(mark(z0)))), MARK(U22(length(z0)))) A__U61(tt, U22(and(z0, z1))) -> c26(A__LENGTH(a__U22(a__and(mark(z0), z1))), MARK(U22(and(z0, z1)))) A__U61(tt, U22(isNatIListKind(z0))) -> c26(A__LENGTH(a__U22(a__isNatIListKind(z0))), MARK(U22(isNatIListKind(z0)))) A__U61(tt, U22(isNatKind(z0))) -> c26(A__LENGTH(a__U22(a__isNatKind(z0))), MARK(U22(isNatKind(z0)))) A__U61(tt, U22(cons(z0, z1))) -> c26(A__LENGTH(a__U22(cons(mark(z0), z1))), MARK(U22(cons(z0, z1)))) A__U61(tt, U22(0)) -> c26(A__LENGTH(a__U22(0)), MARK(U22(0))) A__U61(tt, U22(tt)) -> c26(A__LENGTH(a__U22(tt)), MARK(U22(tt))) A__U61(tt, U22(s(z0))) -> c26(A__LENGTH(a__U22(s(mark(z0)))), MARK(U22(s(z0)))) A__U61(tt, U22(nil)) -> c26(A__LENGTH(a__U22(nil)), MARK(U22(nil))) A__U61(tt, U22(x0)) -> c26(MARK(U22(x0))) A__U61(tt, isNat(length(z0))) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), z0)), MARK(isNat(length(z0)))) A__U61(tt, isNat(s(z0))) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), z0)), MARK(isNat(s(z0)))) A__U61(tt, isNat(0)) -> c26(MARK(isNat(0))) A__U61(tt, isNat(z0)) -> c26(MARK(isNat(z0))) A__U61(tt, U31(zeros, x1)) -> c26(A__LENGTH(a__U31(a__zeros, x1)), MARK(U31(zeros, x1))) A__U61(tt, U31(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U11(mark(z0), z1), x1)), MARK(U31(U11(z0, z1), x1))) A__U61(tt, U31(U12(z0), x1)) -> c26(A__LENGTH(a__U31(a__U12(mark(z0)), x1)), MARK(U31(U12(z0), x1))) A__U61(tt, U31(isNatList(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatList(z0), x1)), MARK(U31(isNatList(z0), x1))) A__U61(tt, U31(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U21(mark(z0), z1), x1)), MARK(U31(U21(z0, z1), x1))) A__U61(tt, U31(U22(z0), x1)) -> c26(A__LENGTH(a__U31(a__U22(mark(z0)), x1)), MARK(U31(U22(z0), x1))) A__U61(tt, U31(isNat(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNat(z0), x1)), MARK(U31(isNat(z0), x1))) A__U61(tt, U31(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U31(mark(z0), z1), x1)), MARK(U31(U31(z0, z1), x1))) A__U61(tt, U31(U32(z0), x1)) -> c26(A__LENGTH(a__U31(a__U32(mark(z0)), x1)), MARK(U31(U32(z0), x1))) A__U61(tt, U31(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(U31(U41(z0, z1, z2), x1))) A__U61(tt, U31(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U42(mark(z0), z1), x1)), MARK(U31(U42(z0, z1), x1))) A__U61(tt, U31(U43(z0), x1)) -> c26(A__LENGTH(a__U31(a__U43(mark(z0)), x1)), MARK(U31(U43(z0), x1))) A__U61(tt, U31(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatIList(z0), x1)), MARK(U31(isNatIList(z0), x1))) A__U61(tt, U31(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U31(a__U51(mark(z0), z1, z2), x1)), MARK(U31(U51(z0, z1, z2), x1))) A__U61(tt, U31(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U52(mark(z0), z1), x1)), MARK(U31(U52(z0, z1), x1))) A__U61(tt, U31(U53(z0), x1)) -> c26(A__LENGTH(a__U31(a__U53(mark(z0)), x1)), MARK(U31(U53(z0), x1))) A__U61(tt, U31(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U61(mark(z0), z1), x1)), MARK(U31(U61(z0, z1), x1))) A__U61(tt, U31(length(z0), x1)) -> c26(A__LENGTH(a__U31(a__length(mark(z0)), x1)), MARK(U31(length(z0), x1))) A__U61(tt, U31(and(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__and(mark(z0), z1), x1)), MARK(U31(and(z0, z1), x1))) A__U61(tt, U31(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatIListKind(z0), x1)), MARK(U31(isNatIListKind(z0), x1))) A__U61(tt, U31(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatKind(z0), x1)), MARK(U31(isNatKind(z0), x1))) A__U61(tt, U31(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U31(cons(mark(z0), z1), x1)), MARK(U31(cons(z0, z1), x1))) A__U61(tt, U31(tt, x1)) -> c26(A__LENGTH(a__U31(tt, x1)), MARK(U31(tt, x1))) A__U61(tt, U31(s(z0), x1)) -> c26(A__LENGTH(a__U31(s(mark(z0)), x1)), MARK(U31(s(z0), x1))) A__U61(tt, U31(x0, z1)) -> c26(MARK(U31(x0, z1))) A__U61(tt, U31(0, x1)) -> c26(A__LENGTH(a__U31(0, x1))) A__U61(tt, U31(nil, x1)) -> c26(A__LENGTH(a__U31(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_1, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c14_2, c20_2 ---------------------------------------- (175) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U61(tt, U32(z0)) -> c26(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) by A__U61(tt, U32(x0)) -> c26(A__LENGTH(U32(mark(x0))), MARK(U32(x0))) A__U61(tt, U32(zeros)) -> c26(A__LENGTH(a__U32(a__zeros)), MARK(U32(zeros))) A__U61(tt, U32(U11(z0, z1))) -> c26(A__LENGTH(a__U32(a__U11(mark(z0), z1))), MARK(U32(U11(z0, z1)))) A__U61(tt, U32(U12(z0))) -> c26(A__LENGTH(a__U32(a__U12(mark(z0)))), MARK(U32(U12(z0)))) A__U61(tt, U32(isNatList(z0))) -> c26(A__LENGTH(a__U32(a__isNatList(z0))), MARK(U32(isNatList(z0)))) A__U61(tt, U32(U21(z0, z1))) -> c26(A__LENGTH(a__U32(a__U21(mark(z0), z1))), MARK(U32(U21(z0, z1)))) A__U61(tt, U32(U22(z0))) -> c26(A__LENGTH(a__U32(a__U22(mark(z0)))), MARK(U32(U22(z0)))) A__U61(tt, U32(isNat(z0))) -> c26(A__LENGTH(a__U32(a__isNat(z0))), MARK(U32(isNat(z0)))) A__U61(tt, U32(U31(z0, z1))) -> c26(A__LENGTH(a__U32(a__U31(mark(z0), z1))), MARK(U32(U31(z0, z1)))) A__U61(tt, U32(U32(z0))) -> c26(A__LENGTH(a__U32(a__U32(mark(z0)))), MARK(U32(U32(z0)))) A__U61(tt, U32(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U32(a__U41(mark(z0), z1, z2))), MARK(U32(U41(z0, z1, z2)))) A__U61(tt, U32(U42(z0, z1))) -> c26(A__LENGTH(a__U32(a__U42(mark(z0), z1))), MARK(U32(U42(z0, z1)))) A__U61(tt, U32(U43(z0))) -> c26(A__LENGTH(a__U32(a__U43(mark(z0)))), MARK(U32(U43(z0)))) A__U61(tt, U32(isNatIList(z0))) -> c26(A__LENGTH(a__U32(a__isNatIList(z0))), MARK(U32(isNatIList(z0)))) A__U61(tt, U32(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U32(a__U51(mark(z0), z1, z2))), MARK(U32(U51(z0, z1, z2)))) A__U61(tt, U32(U52(z0, z1))) -> c26(A__LENGTH(a__U32(a__U52(mark(z0), z1))), MARK(U32(U52(z0, z1)))) A__U61(tt, U32(U53(z0))) -> c26(A__LENGTH(a__U32(a__U53(mark(z0)))), MARK(U32(U53(z0)))) A__U61(tt, U32(U61(z0, z1))) -> c26(A__LENGTH(a__U32(a__U61(mark(z0), z1))), MARK(U32(U61(z0, z1)))) A__U61(tt, U32(length(z0))) -> c26(A__LENGTH(a__U32(a__length(mark(z0)))), MARK(U32(length(z0)))) A__U61(tt, U32(and(z0, z1))) -> c26(A__LENGTH(a__U32(a__and(mark(z0), z1))), MARK(U32(and(z0, z1)))) A__U61(tt, U32(isNatIListKind(z0))) -> c26(A__LENGTH(a__U32(a__isNatIListKind(z0))), MARK(U32(isNatIListKind(z0)))) A__U61(tt, U32(isNatKind(z0))) -> c26(A__LENGTH(a__U32(a__isNatKind(z0))), MARK(U32(isNatKind(z0)))) A__U61(tt, U32(cons(z0, z1))) -> c26(A__LENGTH(a__U32(cons(mark(z0), z1))), MARK(U32(cons(z0, z1)))) A__U61(tt, U32(0)) -> c26(A__LENGTH(a__U32(0)), MARK(U32(0))) A__U61(tt, U32(tt)) -> c26(A__LENGTH(a__U32(tt)), MARK(U32(tt))) A__U61(tt, U32(s(z0))) -> c26(A__LENGTH(a__U32(s(mark(z0)))), MARK(U32(s(z0)))) A__U61(tt, U32(nil)) -> c26(A__LENGTH(a__U32(nil)), MARK(U32(nil))) A__U61(tt, U32(x0)) -> c26(MARK(U32(x0))) ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> 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c26(A__LENGTH(a__U32(a__isNatIList(z0))), MARK(U32(isNatIList(z0)))) A__U61(tt, U32(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U32(a__U51(mark(z0), z1, z2))), MARK(U32(U51(z0, z1, z2)))) A__U61(tt, U32(U52(z0, z1))) -> c26(A__LENGTH(a__U32(a__U52(mark(z0), z1))), MARK(U32(U52(z0, z1)))) A__U61(tt, U32(U53(z0))) -> c26(A__LENGTH(a__U32(a__U53(mark(z0)))), MARK(U32(U53(z0)))) A__U61(tt, U32(U61(z0, z1))) -> c26(A__LENGTH(a__U32(a__U61(mark(z0), z1))), MARK(U32(U61(z0, z1)))) A__U61(tt, U32(length(z0))) -> c26(A__LENGTH(a__U32(a__length(mark(z0)))), MARK(U32(length(z0)))) A__U61(tt, U32(and(z0, z1))) -> c26(A__LENGTH(a__U32(a__and(mark(z0), z1))), MARK(U32(and(z0, z1)))) A__U61(tt, U32(isNatIListKind(z0))) -> c26(A__LENGTH(a__U32(a__isNatIListKind(z0))), MARK(U32(isNatIListKind(z0)))) A__U61(tt, U32(isNatKind(z0))) -> c26(A__LENGTH(a__U32(a__isNatKind(z0))), MARK(U32(isNatKind(z0)))) A__U61(tt, U32(cons(z0, z1))) -> c26(A__LENGTH(a__U32(cons(mark(z0), z1))), MARK(U32(cons(z0, z1)))) A__U61(tt, U32(0)) -> c26(A__LENGTH(a__U32(0)), MARK(U32(0))) A__U61(tt, U32(tt)) -> c26(A__LENGTH(a__U32(tt)), MARK(U32(tt))) A__U61(tt, U32(s(z0))) -> c26(A__LENGTH(a__U32(s(mark(z0)))), MARK(U32(s(z0)))) A__U61(tt, U32(nil)) -> c26(A__LENGTH(a__U32(nil)), MARK(U32(nil))) A__U61(tt, U32(x0)) -> c26(MARK(U32(x0))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> c26(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U61(tt, U12(U21(z0, z1))) -> c26(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U61(tt, U12(U22(z0))) -> c26(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U61(tt, U12(isNat(z0))) -> c26(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U61(tt, U12(U31(z0, z1))) -> c26(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U61(tt, U12(U32(z0))) -> c26(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U61(tt, U12(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U61(tt, U12(U42(z0, z1))) -> c26(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U61(tt, U12(U43(z0))) -> c26(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U61(tt, U12(isNatIList(z0))) -> c26(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U61(tt, U12(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U61(tt, U12(U52(z0, z1))) -> c26(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U61(tt, U12(U53(z0))) -> c26(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U61(tt, U12(U61(z0, z1))) -> c26(A__LENGTH(a__U12(a__U61(mark(z0), z1))), MARK(U12(U61(z0, z1)))) A__U61(tt, U12(length(z0))) -> c26(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U61(tt, U12(and(z0, z1))) -> c26(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U61(tt, U12(isNatIListKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U61(tt, U12(isNatKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U61(tt, U12(cons(z0, z1))) -> c26(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U61(tt, U12(0)) -> c26(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U61(tt, U12(tt)) -> c26(A__LENGTH(a__U12(tt)), MARK(U12(tt))) A__U61(tt, U12(s(z0))) -> c26(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U61(tt, U12(nil)) -> c26(A__LENGTH(a__U12(nil)), MARK(U12(nil))) A__U61(tt, U12(x0)) -> c26(MARK(U12(x0))) A__U61(tt, isNatList(cons(z0, z1))) -> c26(A__LENGTH(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(cons(z0, z1)))) A__U61(tt, isNatList(nil)) -> c26(MARK(isNatList(nil))) A__U61(tt, isNatList(z0)) -> c26(MARK(isNatList(z0))) A__U61(tt, U21(zeros, x1)) -> c26(A__LENGTH(a__U21(a__zeros, x1)), MARK(U21(zeros, x1))) A__U61(tt, U21(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1)), MARK(U21(U11(z0, z1), x1))) A__U61(tt, U21(U12(z0), x1)) -> c26(A__LENGTH(a__U21(a__U12(mark(z0)), x1)), MARK(U21(U12(z0), x1))) A__U61(tt, U21(isNatList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatList(z0), x1)), MARK(U21(isNatList(z0), x1))) A__U61(tt, U21(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U21(mark(z0), z1), x1)), MARK(U21(U21(z0, z1), x1))) A__U61(tt, U21(U22(z0), x1)) -> c26(A__LENGTH(a__U21(a__U22(mark(z0)), x1)), MARK(U21(U22(z0), x1))) A__U61(tt, U21(isNat(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNat(z0), x1)), MARK(U21(isNat(z0), x1))) A__U61(tt, U21(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U31(mark(z0), z1), x1)), MARK(U21(U31(z0, z1), x1))) A__U61(tt, U21(U32(z0), x1)) -> c26(A__LENGTH(a__U21(a__U32(mark(z0)), x1)), MARK(U21(U32(z0), x1))) A__U61(tt, U21(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(U21(U41(z0, z1, z2), x1))) A__U61(tt, U21(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U42(mark(z0), z1), x1)), MARK(U21(U42(z0, z1), x1))) A__U61(tt, U21(U43(z0), x1)) -> c26(A__LENGTH(a__U21(a__U43(mark(z0)), x1)), MARK(U21(U43(z0), x1))) A__U61(tt, U21(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIList(z0), x1)), MARK(U21(isNatIList(z0), x1))) A__U61(tt, U21(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U51(mark(z0), z1, z2), x1)), MARK(U21(U51(z0, z1, z2), x1))) A__U61(tt, U21(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U52(mark(z0), z1), x1)), MARK(U21(U52(z0, z1), x1))) A__U61(tt, U21(U53(z0), x1)) -> c26(A__LENGTH(a__U21(a__U53(mark(z0)), x1)), MARK(U21(U53(z0), x1))) A__U61(tt, U21(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U61(mark(z0), z1), x1)), MARK(U21(U61(z0, z1), x1))) A__U61(tt, U21(length(z0), x1)) -> c26(A__LENGTH(a__U21(a__length(mark(z0)), x1)), MARK(U21(length(z0), x1))) A__U61(tt, U21(and(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__and(mark(z0), z1), x1)), MARK(U21(and(z0, z1), x1))) A__U61(tt, U21(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIListKind(z0), x1)), MARK(U21(isNatIListKind(z0), x1))) A__U61(tt, U21(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), x1)), MARK(U21(isNatKind(z0), x1))) A__U61(tt, U21(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U21(cons(mark(z0), z1), x1)), MARK(U21(cons(z0, z1), x1))) A__U61(tt, U21(tt, x1)) -> c26(A__LENGTH(a__U21(tt, x1)), MARK(U21(tt, x1))) A__U61(tt, U21(s(z0), x1)) -> c26(A__LENGTH(a__U21(s(mark(z0)), x1)), MARK(U21(s(z0), x1))) A__U61(tt, U21(x0, z1)) -> c26(MARK(U21(x0, z1))) A__U61(tt, U21(0, x1)) -> c26(A__LENGTH(a__U21(0, x1))) A__U61(tt, U21(nil, x1)) -> c26(A__LENGTH(a__U21(nil, x1))) A__U61(tt, U22(zeros)) -> c26(A__LENGTH(a__U22(a__zeros)), MARK(U22(zeros))) A__U61(tt, U22(U11(z0, z1))) -> c26(A__LENGTH(a__U22(a__U11(mark(z0), z1))), MARK(U22(U11(z0, z1)))) A__U61(tt, U22(U12(z0))) -> c26(A__LENGTH(a__U22(a__U12(mark(z0)))), MARK(U22(U12(z0)))) A__U61(tt, U22(isNatList(z0))) -> c26(A__LENGTH(a__U22(a__isNatList(z0))), MARK(U22(isNatList(z0)))) A__U61(tt, U22(U21(z0, z1))) -> c26(A__LENGTH(a__U22(a__U21(mark(z0), z1))), MARK(U22(U21(z0, z1)))) A__U61(tt, U22(U22(z0))) -> c26(A__LENGTH(a__U22(a__U22(mark(z0)))), MARK(U22(U22(z0)))) A__U61(tt, U22(isNat(z0))) -> c26(A__LENGTH(a__U22(a__isNat(z0))), MARK(U22(isNat(z0)))) A__U61(tt, U22(U31(z0, z1))) -> c26(A__LENGTH(a__U22(a__U31(mark(z0), z1))), MARK(U22(U31(z0, z1)))) A__U61(tt, U22(U32(z0))) -> c26(A__LENGTH(a__U22(a__U32(mark(z0)))), MARK(U22(U32(z0)))) A__U61(tt, U22(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U22(a__U41(mark(z0), z1, z2))), MARK(U22(U41(z0, z1, z2)))) A__U61(tt, U22(U42(z0, z1))) -> c26(A__LENGTH(a__U22(a__U42(mark(z0), z1))), MARK(U22(U42(z0, z1)))) A__U61(tt, U22(U43(z0))) -> c26(A__LENGTH(a__U22(a__U43(mark(z0)))), MARK(U22(U43(z0)))) A__U61(tt, U22(isNatIList(z0))) -> c26(A__LENGTH(a__U22(a__isNatIList(z0))), MARK(U22(isNatIList(z0)))) A__U61(tt, U22(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U22(a__U51(mark(z0), z1, z2))), MARK(U22(U51(z0, z1, z2)))) A__U61(tt, U22(U52(z0, z1))) -> c26(A__LENGTH(a__U22(a__U52(mark(z0), z1))), MARK(U22(U52(z0, z1)))) A__U61(tt, U22(U53(z0))) -> c26(A__LENGTH(a__U22(a__U53(mark(z0)))), MARK(U22(U53(z0)))) A__U61(tt, U22(U61(z0, z1))) -> c26(A__LENGTH(a__U22(a__U61(mark(z0), z1))), MARK(U22(U61(z0, z1)))) A__U61(tt, U22(length(z0))) -> c26(A__LENGTH(a__U22(a__length(mark(z0)))), MARK(U22(length(z0)))) A__U61(tt, U22(and(z0, z1))) -> c26(A__LENGTH(a__U22(a__and(mark(z0), z1))), MARK(U22(and(z0, z1)))) A__U61(tt, U22(isNatIListKind(z0))) -> c26(A__LENGTH(a__U22(a__isNatIListKind(z0))), MARK(U22(isNatIListKind(z0)))) A__U61(tt, U22(isNatKind(z0))) -> c26(A__LENGTH(a__U22(a__isNatKind(z0))), MARK(U22(isNatKind(z0)))) A__U61(tt, U22(cons(z0, z1))) -> c26(A__LENGTH(a__U22(cons(mark(z0), z1))), MARK(U22(cons(z0, z1)))) A__U61(tt, U22(0)) -> c26(A__LENGTH(a__U22(0)), MARK(U22(0))) A__U61(tt, U22(tt)) -> c26(A__LENGTH(a__U22(tt)), MARK(U22(tt))) A__U61(tt, U22(s(z0))) -> c26(A__LENGTH(a__U22(s(mark(z0)))), MARK(U22(s(z0)))) A__U61(tt, U22(nil)) -> c26(A__LENGTH(a__U22(nil)), MARK(U22(nil))) A__U61(tt, U22(x0)) -> c26(MARK(U22(x0))) A__U61(tt, isNat(length(z0))) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), z0)), MARK(isNat(length(z0)))) A__U61(tt, isNat(s(z0))) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), z0)), MARK(isNat(s(z0)))) A__U61(tt, isNat(0)) -> c26(MARK(isNat(0))) A__U61(tt, isNat(z0)) -> c26(MARK(isNat(z0))) A__U61(tt, U31(zeros, x1)) -> c26(A__LENGTH(a__U31(a__zeros, x1)), MARK(U31(zeros, x1))) A__U61(tt, U31(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U11(mark(z0), z1), x1)), MARK(U31(U11(z0, z1), x1))) A__U61(tt, U31(U12(z0), x1)) -> c26(A__LENGTH(a__U31(a__U12(mark(z0)), x1)), MARK(U31(U12(z0), x1))) A__U61(tt, U31(isNatList(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatList(z0), x1)), MARK(U31(isNatList(z0), x1))) A__U61(tt, U31(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U21(mark(z0), z1), x1)), MARK(U31(U21(z0, z1), x1))) A__U61(tt, U31(U22(z0), x1)) -> c26(A__LENGTH(a__U31(a__U22(mark(z0)), x1)), MARK(U31(U22(z0), x1))) A__U61(tt, U31(isNat(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNat(z0), x1)), MARK(U31(isNat(z0), x1))) A__U61(tt, U31(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U31(mark(z0), z1), x1)), MARK(U31(U31(z0, z1), x1))) A__U61(tt, U31(U32(z0), x1)) -> c26(A__LENGTH(a__U31(a__U32(mark(z0)), x1)), MARK(U31(U32(z0), x1))) A__U61(tt, U31(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(U31(U41(z0, z1, z2), x1))) A__U61(tt, U31(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U42(mark(z0), z1), x1)), MARK(U31(U42(z0, z1), x1))) A__U61(tt, U31(U43(z0), x1)) -> c26(A__LENGTH(a__U31(a__U43(mark(z0)), x1)), MARK(U31(U43(z0), x1))) A__U61(tt, U31(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatIList(z0), x1)), MARK(U31(isNatIList(z0), x1))) A__U61(tt, U31(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U31(a__U51(mark(z0), z1, z2), x1)), MARK(U31(U51(z0, z1, z2), x1))) A__U61(tt, U31(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U52(mark(z0), z1), x1)), MARK(U31(U52(z0, z1), x1))) A__U61(tt, U31(U53(z0), x1)) -> c26(A__LENGTH(a__U31(a__U53(mark(z0)), x1)), MARK(U31(U53(z0), x1))) A__U61(tt, U31(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U61(mark(z0), z1), x1)), MARK(U31(U61(z0, z1), x1))) A__U61(tt, U31(length(z0), x1)) -> c26(A__LENGTH(a__U31(a__length(mark(z0)), x1)), MARK(U31(length(z0), x1))) A__U61(tt, U31(and(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__and(mark(z0), z1), x1)), MARK(U31(and(z0, z1), x1))) A__U61(tt, U31(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatIListKind(z0), x1)), MARK(U31(isNatIListKind(z0), x1))) A__U61(tt, U31(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatKind(z0), x1)), MARK(U31(isNatKind(z0), x1))) A__U61(tt, U31(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U31(cons(mark(z0), z1), x1)), MARK(U31(cons(z0, z1), x1))) A__U61(tt, U31(tt, x1)) -> c26(A__LENGTH(a__U31(tt, x1)), MARK(U31(tt, x1))) A__U61(tt, U31(s(z0), x1)) -> c26(A__LENGTH(a__U31(s(mark(z0)), x1)), MARK(U31(s(z0), x1))) A__U61(tt, U31(x0, z1)) -> c26(MARK(U31(x0, z1))) A__U61(tt, U31(0, x1)) -> c26(A__LENGTH(a__U31(0, x1))) A__U61(tt, U31(nil, x1)) -> c26(A__LENGTH(a__U31(nil, x1))) A__U61(tt, U32(x0)) -> c26(A__LENGTH(U32(mark(x0))), MARK(U32(x0))) A__U61(tt, U32(zeros)) -> c26(A__LENGTH(a__U32(a__zeros)), MARK(U32(zeros))) A__U61(tt, U32(U11(z0, z1))) -> c26(A__LENGTH(a__U32(a__U11(mark(z0), z1))), MARK(U32(U11(z0, z1)))) A__U61(tt, U32(U12(z0))) -> c26(A__LENGTH(a__U32(a__U12(mark(z0)))), MARK(U32(U12(z0)))) A__U61(tt, U32(isNatList(z0))) -> c26(A__LENGTH(a__U32(a__isNatList(z0))), MARK(U32(isNatList(z0)))) A__U61(tt, U32(U21(z0, z1))) -> c26(A__LENGTH(a__U32(a__U21(mark(z0), z1))), MARK(U32(U21(z0, z1)))) A__U61(tt, U32(U22(z0))) -> c26(A__LENGTH(a__U32(a__U22(mark(z0)))), MARK(U32(U22(z0)))) A__U61(tt, U32(isNat(z0))) -> c26(A__LENGTH(a__U32(a__isNat(z0))), MARK(U32(isNat(z0)))) A__U61(tt, U32(U31(z0, z1))) -> c26(A__LENGTH(a__U32(a__U31(mark(z0), z1))), MARK(U32(U31(z0, z1)))) A__U61(tt, U32(U32(z0))) -> c26(A__LENGTH(a__U32(a__U32(mark(z0)))), MARK(U32(U32(z0)))) A__U61(tt, U32(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U32(a__U41(mark(z0), z1, z2))), MARK(U32(U41(z0, z1, z2)))) A__U61(tt, U32(U42(z0, z1))) -> c26(A__LENGTH(a__U32(a__U42(mark(z0), z1))), MARK(U32(U42(z0, z1)))) A__U61(tt, U32(U43(z0))) -> c26(A__LENGTH(a__U32(a__U43(mark(z0)))), MARK(U32(U43(z0)))) A__U61(tt, U32(isNatIList(z0))) -> c26(A__LENGTH(a__U32(a__isNatIList(z0))), MARK(U32(isNatIList(z0)))) A__U61(tt, U32(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U32(a__U51(mark(z0), z1, z2))), MARK(U32(U51(z0, z1, z2)))) A__U61(tt, U32(U52(z0, z1))) -> c26(A__LENGTH(a__U32(a__U52(mark(z0), z1))), MARK(U32(U52(z0, z1)))) A__U61(tt, U32(U53(z0))) -> c26(A__LENGTH(a__U32(a__U53(mark(z0)))), MARK(U32(U53(z0)))) A__U61(tt, U32(U61(z0, z1))) -> c26(A__LENGTH(a__U32(a__U61(mark(z0), z1))), MARK(U32(U61(z0, z1)))) A__U61(tt, U32(length(z0))) -> c26(A__LENGTH(a__U32(a__length(mark(z0)))), MARK(U32(length(z0)))) A__U61(tt, U32(and(z0, z1))) -> c26(A__LENGTH(a__U32(a__and(mark(z0), z1))), MARK(U32(and(z0, z1)))) A__U61(tt, U32(isNatIListKind(z0))) -> c26(A__LENGTH(a__U32(a__isNatIListKind(z0))), MARK(U32(isNatIListKind(z0)))) A__U61(tt, U32(isNatKind(z0))) -> c26(A__LENGTH(a__U32(a__isNatKind(z0))), MARK(U32(isNatKind(z0)))) A__U61(tt, U32(cons(z0, z1))) -> c26(A__LENGTH(a__U32(cons(mark(z0), z1))), MARK(U32(cons(z0, z1)))) A__U61(tt, U32(0)) -> c26(A__LENGTH(a__U32(0)), MARK(U32(0))) A__U61(tt, U32(tt)) -> c26(A__LENGTH(a__U32(tt)), MARK(U32(tt))) A__U61(tt, U32(s(z0))) -> c26(A__LENGTH(a__U32(s(mark(z0)))), MARK(U32(s(z0)))) A__U61(tt, U32(nil)) -> c26(A__LENGTH(a__U32(nil)), MARK(U32(nil))) A__U61(tt, U32(x0)) -> c26(MARK(U32(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_1, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c14_2, c20_2 ---------------------------------------- (177) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), 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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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> c26(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U61(tt, U12(U21(z0, z1))) -> c26(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U61(tt, U12(U22(z0))) -> 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A__U61(tt, isNatList(cons(z0, z1))) -> c26(A__LENGTH(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(cons(z0, z1)))) A__U61(tt, isNatList(nil)) -> c26(MARK(isNatList(nil))) A__U61(tt, isNatList(z0)) -> c26(MARK(isNatList(z0))) A__U61(tt, U21(zeros, x1)) -> c26(A__LENGTH(a__U21(a__zeros, x1)), MARK(U21(zeros, x1))) A__U61(tt, U21(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1)), MARK(U21(U11(z0, z1), x1))) A__U61(tt, U21(U12(z0), x1)) -> c26(A__LENGTH(a__U21(a__U12(mark(z0)), x1)), MARK(U21(U12(z0), x1))) A__U61(tt, U21(isNatList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatList(z0), x1)), MARK(U21(isNatList(z0), x1))) A__U61(tt, U21(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U21(mark(z0), z1), x1)), MARK(U21(U21(z0, z1), x1))) A__U61(tt, U21(U22(z0), x1)) -> c26(A__LENGTH(a__U21(a__U22(mark(z0)), x1)), MARK(U21(U22(z0), x1))) A__U61(tt, U21(isNat(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNat(z0), x1)), MARK(U21(isNat(z0), x1))) A__U61(tt, U21(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U31(mark(z0), z1), x1)), MARK(U21(U31(z0, z1), x1))) A__U61(tt, U21(U32(z0), x1)) -> c26(A__LENGTH(a__U21(a__U32(mark(z0)), x1)), MARK(U21(U32(z0), x1))) A__U61(tt, U21(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(U21(U41(z0, z1, z2), x1))) A__U61(tt, U21(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U42(mark(z0), z1), x1)), MARK(U21(U42(z0, z1), x1))) A__U61(tt, U21(U43(z0), x1)) -> c26(A__LENGTH(a__U21(a__U43(mark(z0)), x1)), MARK(U21(U43(z0), x1))) A__U61(tt, U21(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIList(z0), x1)), MARK(U21(isNatIList(z0), x1))) A__U61(tt, U21(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U51(mark(z0), z1, z2), x1)), MARK(U21(U51(z0, z1, z2), x1))) A__U61(tt, U21(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U52(mark(z0), z1), x1)), MARK(U21(U52(z0, z1), x1))) A__U61(tt, U21(U53(z0), x1)) -> c26(A__LENGTH(a__U21(a__U53(mark(z0)), x1)), MARK(U21(U53(z0), x1))) A__U61(tt, U21(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U61(mark(z0), z1), x1)), MARK(U21(U61(z0, z1), x1))) A__U61(tt, U21(length(z0), x1)) -> c26(A__LENGTH(a__U21(a__length(mark(z0)), x1)), MARK(U21(length(z0), x1))) A__U61(tt, U21(and(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__and(mark(z0), z1), x1)), MARK(U21(and(z0, z1), x1))) A__U61(tt, U21(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIListKind(z0), x1)), MARK(U21(isNatIListKind(z0), x1))) A__U61(tt, U21(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), x1)), MARK(U21(isNatKind(z0), x1))) A__U61(tt, U21(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U21(cons(mark(z0), z1), x1)), MARK(U21(cons(z0, z1), x1))) A__U61(tt, U21(tt, x1)) -> c26(A__LENGTH(a__U21(tt, x1)), MARK(U21(tt, x1))) A__U61(tt, U21(s(z0), x1)) -> c26(A__LENGTH(a__U21(s(mark(z0)), x1)), MARK(U21(s(z0), x1))) A__U61(tt, U21(x0, z1)) -> c26(MARK(U21(x0, z1))) A__U61(tt, U21(0, x1)) -> c26(A__LENGTH(a__U21(0, x1))) A__U61(tt, U21(nil, x1)) -> c26(A__LENGTH(a__U21(nil, x1))) A__U61(tt, U22(zeros)) -> c26(A__LENGTH(a__U22(a__zeros)), MARK(U22(zeros))) A__U61(tt, U22(U11(z0, z1))) -> c26(A__LENGTH(a__U22(a__U11(mark(z0), z1))), MARK(U22(U11(z0, z1)))) A__U61(tt, U22(U12(z0))) -> c26(A__LENGTH(a__U22(a__U12(mark(z0)))), MARK(U22(U12(z0)))) A__U61(tt, U22(isNatList(z0))) -> c26(A__LENGTH(a__U22(a__isNatList(z0))), MARK(U22(isNatList(z0)))) A__U61(tt, U22(U21(z0, z1))) -> c26(A__LENGTH(a__U22(a__U21(mark(z0), z1))), MARK(U22(U21(z0, z1)))) A__U61(tt, U22(U22(z0))) -> c26(A__LENGTH(a__U22(a__U22(mark(z0)))), MARK(U22(U22(z0)))) A__U61(tt, U22(isNat(z0))) -> c26(A__LENGTH(a__U22(a__isNat(z0))), MARK(U22(isNat(z0)))) A__U61(tt, U22(U31(z0, z1))) -> c26(A__LENGTH(a__U22(a__U31(mark(z0), z1))), MARK(U22(U31(z0, z1)))) A__U61(tt, U22(U32(z0))) -> c26(A__LENGTH(a__U22(a__U32(mark(z0)))), MARK(U22(U32(z0)))) A__U61(tt, U22(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U22(a__U41(mark(z0), z1, z2))), MARK(U22(U41(z0, z1, z2)))) A__U61(tt, U22(U42(z0, z1))) -> c26(A__LENGTH(a__U22(a__U42(mark(z0), z1))), MARK(U22(U42(z0, z1)))) A__U61(tt, U22(U43(z0))) -> c26(A__LENGTH(a__U22(a__U43(mark(z0)))), MARK(U22(U43(z0)))) A__U61(tt, U22(isNatIList(z0))) -> c26(A__LENGTH(a__U22(a__isNatIList(z0))), MARK(U22(isNatIList(z0)))) A__U61(tt, U22(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U22(a__U51(mark(z0), z1, z2))), MARK(U22(U51(z0, z1, z2)))) A__U61(tt, U22(U52(z0, z1))) -> c26(A__LENGTH(a__U22(a__U52(mark(z0), z1))), MARK(U22(U52(z0, z1)))) A__U61(tt, U22(U53(z0))) -> c26(A__LENGTH(a__U22(a__U53(mark(z0)))), MARK(U22(U53(z0)))) A__U61(tt, U22(U61(z0, z1))) -> c26(A__LENGTH(a__U22(a__U61(mark(z0), z1))), MARK(U22(U61(z0, z1)))) A__U61(tt, U22(length(z0))) -> c26(A__LENGTH(a__U22(a__length(mark(z0)))), MARK(U22(length(z0)))) A__U61(tt, U22(and(z0, z1))) -> c26(A__LENGTH(a__U22(a__and(mark(z0), z1))), MARK(U22(and(z0, z1)))) A__U61(tt, U22(isNatIListKind(z0))) -> c26(A__LENGTH(a__U22(a__isNatIListKind(z0))), MARK(U22(isNatIListKind(z0)))) A__U61(tt, U22(isNatKind(z0))) -> c26(A__LENGTH(a__U22(a__isNatKind(z0))), MARK(U22(isNatKind(z0)))) A__U61(tt, U22(cons(z0, z1))) -> c26(A__LENGTH(a__U22(cons(mark(z0), z1))), MARK(U22(cons(z0, z1)))) A__U61(tt, U22(0)) -> c26(A__LENGTH(a__U22(0)), MARK(U22(0))) A__U61(tt, U22(tt)) -> c26(A__LENGTH(a__U22(tt)), MARK(U22(tt))) A__U61(tt, U22(s(z0))) -> c26(A__LENGTH(a__U22(s(mark(z0)))), MARK(U22(s(z0)))) A__U61(tt, U22(nil)) -> c26(A__LENGTH(a__U22(nil)), MARK(U22(nil))) A__U61(tt, U22(x0)) -> c26(MARK(U22(x0))) A__U61(tt, isNat(length(z0))) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), z0)), MARK(isNat(length(z0)))) A__U61(tt, isNat(s(z0))) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), z0)), MARK(isNat(s(z0)))) A__U61(tt, isNat(0)) -> c26(MARK(isNat(0))) A__U61(tt, isNat(z0)) -> c26(MARK(isNat(z0))) A__U61(tt, U31(zeros, x1)) -> c26(A__LENGTH(a__U31(a__zeros, x1)), MARK(U31(zeros, x1))) A__U61(tt, U31(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U11(mark(z0), z1), x1)), MARK(U31(U11(z0, z1), x1))) A__U61(tt, U31(U12(z0), x1)) -> c26(A__LENGTH(a__U31(a__U12(mark(z0)), x1)), MARK(U31(U12(z0), x1))) A__U61(tt, U31(isNatList(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatList(z0), x1)), MARK(U31(isNatList(z0), x1))) A__U61(tt, U31(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U21(mark(z0), z1), x1)), MARK(U31(U21(z0, z1), x1))) A__U61(tt, U31(U22(z0), x1)) -> c26(A__LENGTH(a__U31(a__U22(mark(z0)), x1)), MARK(U31(U22(z0), x1))) A__U61(tt, U31(isNat(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNat(z0), x1)), MARK(U31(isNat(z0), x1))) A__U61(tt, U31(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U31(mark(z0), z1), x1)), MARK(U31(U31(z0, z1), x1))) A__U61(tt, U31(U32(z0), x1)) -> c26(A__LENGTH(a__U31(a__U32(mark(z0)), x1)), MARK(U31(U32(z0), x1))) A__U61(tt, U31(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(U31(U41(z0, z1, z2), x1))) A__U61(tt, U31(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U42(mark(z0), z1), x1)), MARK(U31(U42(z0, z1), x1))) A__U61(tt, U31(U43(z0), x1)) -> c26(A__LENGTH(a__U31(a__U43(mark(z0)), x1)), MARK(U31(U43(z0), x1))) A__U61(tt, U31(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatIList(z0), x1)), MARK(U31(isNatIList(z0), x1))) A__U61(tt, U31(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U31(a__U51(mark(z0), z1, z2), x1)), MARK(U31(U51(z0, z1, z2), x1))) A__U61(tt, U31(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U52(mark(z0), z1), x1)), MARK(U31(U52(z0, z1), x1))) A__U61(tt, U31(U53(z0), x1)) -> c26(A__LENGTH(a__U31(a__U53(mark(z0)), x1)), MARK(U31(U53(z0), x1))) A__U61(tt, U31(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U61(mark(z0), z1), x1)), MARK(U31(U61(z0, z1), x1))) A__U61(tt, U31(length(z0), x1)) -> c26(A__LENGTH(a__U31(a__length(mark(z0)), x1)), MARK(U31(length(z0), x1))) A__U61(tt, U31(and(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__and(mark(z0), z1), x1)), MARK(U31(and(z0, z1), x1))) A__U61(tt, U31(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatIListKind(z0), x1)), MARK(U31(isNatIListKind(z0), x1))) A__U61(tt, U31(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatKind(z0), x1)), MARK(U31(isNatKind(z0), x1))) A__U61(tt, U31(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U31(cons(mark(z0), z1), x1)), MARK(U31(cons(z0, z1), x1))) A__U61(tt, U31(tt, x1)) -> c26(A__LENGTH(a__U31(tt, x1)), MARK(U31(tt, x1))) A__U61(tt, U31(s(z0), x1)) -> c26(A__LENGTH(a__U31(s(mark(z0)), x1)), MARK(U31(s(z0), x1))) A__U61(tt, U31(x0, z1)) -> c26(MARK(U31(x0, z1))) A__U61(tt, U31(0, x1)) -> c26(A__LENGTH(a__U31(0, x1))) A__U61(tt, U31(nil, x1)) -> c26(A__LENGTH(a__U31(nil, x1))) A__U61(tt, U32(zeros)) -> c26(A__LENGTH(a__U32(a__zeros)), MARK(U32(zeros))) A__U61(tt, U32(U11(z0, z1))) -> c26(A__LENGTH(a__U32(a__U11(mark(z0), z1))), MARK(U32(U11(z0, z1)))) A__U61(tt, U32(U12(z0))) -> c26(A__LENGTH(a__U32(a__U12(mark(z0)))), MARK(U32(U12(z0)))) A__U61(tt, U32(isNatList(z0))) -> c26(A__LENGTH(a__U32(a__isNatList(z0))), MARK(U32(isNatList(z0)))) A__U61(tt, U32(U21(z0, z1))) -> c26(A__LENGTH(a__U32(a__U21(mark(z0), z1))), MARK(U32(U21(z0, z1)))) A__U61(tt, U32(U22(z0))) -> c26(A__LENGTH(a__U32(a__U22(mark(z0)))), MARK(U32(U22(z0)))) A__U61(tt, U32(isNat(z0))) -> c26(A__LENGTH(a__U32(a__isNat(z0))), MARK(U32(isNat(z0)))) A__U61(tt, U32(U31(z0, z1))) -> c26(A__LENGTH(a__U32(a__U31(mark(z0), z1))), MARK(U32(U31(z0, z1)))) A__U61(tt, U32(U32(z0))) -> c26(A__LENGTH(a__U32(a__U32(mark(z0)))), MARK(U32(U32(z0)))) A__U61(tt, U32(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U32(a__U41(mark(z0), z1, z2))), MARK(U32(U41(z0, z1, z2)))) A__U61(tt, U32(U42(z0, z1))) -> c26(A__LENGTH(a__U32(a__U42(mark(z0), z1))), MARK(U32(U42(z0, z1)))) A__U61(tt, U32(U43(z0))) -> c26(A__LENGTH(a__U32(a__U43(mark(z0)))), MARK(U32(U43(z0)))) A__U61(tt, U32(isNatIList(z0))) -> c26(A__LENGTH(a__U32(a__isNatIList(z0))), MARK(U32(isNatIList(z0)))) A__U61(tt, U32(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U32(a__U51(mark(z0), z1, z2))), MARK(U32(U51(z0, z1, z2)))) A__U61(tt, U32(U52(z0, z1))) -> c26(A__LENGTH(a__U32(a__U52(mark(z0), z1))), MARK(U32(U52(z0, z1)))) A__U61(tt, U32(U53(z0))) -> c26(A__LENGTH(a__U32(a__U53(mark(z0)))), MARK(U32(U53(z0)))) A__U61(tt, U32(U61(z0, z1))) -> c26(A__LENGTH(a__U32(a__U61(mark(z0), z1))), MARK(U32(U61(z0, z1)))) A__U61(tt, U32(length(z0))) -> c26(A__LENGTH(a__U32(a__length(mark(z0)))), MARK(U32(length(z0)))) A__U61(tt, U32(and(z0, z1))) -> c26(A__LENGTH(a__U32(a__and(mark(z0), z1))), MARK(U32(and(z0, z1)))) A__U61(tt, U32(isNatIListKind(z0))) -> c26(A__LENGTH(a__U32(a__isNatIListKind(z0))), MARK(U32(isNatIListKind(z0)))) A__U61(tt, U32(isNatKind(z0))) -> c26(A__LENGTH(a__U32(a__isNatKind(z0))), MARK(U32(isNatKind(z0)))) A__U61(tt, U32(cons(z0, z1))) -> c26(A__LENGTH(a__U32(cons(mark(z0), z1))), MARK(U32(cons(z0, z1)))) A__U61(tt, U32(0)) -> c26(A__LENGTH(a__U32(0)), MARK(U32(0))) A__U61(tt, U32(tt)) -> c26(A__LENGTH(a__U32(tt)), MARK(U32(tt))) A__U61(tt, U32(s(z0))) -> c26(A__LENGTH(a__U32(s(mark(z0)))), MARK(U32(s(z0)))) A__U61(tt, U32(nil)) -> c26(A__LENGTH(a__U32(nil)), MARK(U32(nil))) A__U61(tt, U32(x0)) -> c26(MARK(U32(x0))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, 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MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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, 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U22(isNatKind(z0))) -> c26(A__LENGTH(a__U22(a__isNatKind(z0))), MARK(U22(isNatKind(z0)))) A__U61(tt, U22(cons(z0, z1))) -> c26(A__LENGTH(a__U22(cons(mark(z0), z1))), MARK(U22(cons(z0, z1)))) A__U61(tt, U22(0)) -> c26(A__LENGTH(a__U22(0)), MARK(U22(0))) A__U61(tt, U22(tt)) -> c26(A__LENGTH(a__U22(tt)), MARK(U22(tt))) A__U61(tt, U22(s(z0))) -> c26(A__LENGTH(a__U22(s(mark(z0)))), MARK(U22(s(z0)))) A__U61(tt, U22(nil)) -> c26(A__LENGTH(a__U22(nil)), MARK(U22(nil))) A__U61(tt, U22(x0)) -> c26(MARK(U22(x0))) A__U61(tt, isNat(length(z0))) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), z0)), MARK(isNat(length(z0)))) A__U61(tt, isNat(s(z0))) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), z0)), MARK(isNat(s(z0)))) A__U61(tt, isNat(0)) -> c26(MARK(isNat(0))) A__U61(tt, isNat(z0)) -> c26(MARK(isNat(z0))) A__U61(tt, U31(zeros, x1)) -> c26(A__LENGTH(a__U31(a__zeros, x1)), MARK(U31(zeros, x1))) A__U61(tt, U31(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U11(mark(z0), z1), x1)), MARK(U31(U11(z0, z1), x1))) A__U61(tt, U31(U12(z0), x1)) -> c26(A__LENGTH(a__U31(a__U12(mark(z0)), x1)), MARK(U31(U12(z0), x1))) A__U61(tt, U31(isNatList(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatList(z0), x1)), MARK(U31(isNatList(z0), x1))) A__U61(tt, U31(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U21(mark(z0), z1), x1)), MARK(U31(U21(z0, z1), x1))) A__U61(tt, U31(U22(z0), x1)) -> c26(A__LENGTH(a__U31(a__U22(mark(z0)), x1)), MARK(U31(U22(z0), x1))) A__U61(tt, U31(isNat(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNat(z0), x1)), MARK(U31(isNat(z0), x1))) A__U61(tt, U31(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U31(mark(z0), z1), x1)), MARK(U31(U31(z0, z1), x1))) A__U61(tt, U31(U32(z0), x1)) -> c26(A__LENGTH(a__U31(a__U32(mark(z0)), x1)), MARK(U31(U32(z0), x1))) A__U61(tt, U31(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(U31(U41(z0, z1, z2), x1))) A__U61(tt, U31(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U42(mark(z0), z1), x1)), MARK(U31(U42(z0, z1), x1))) A__U61(tt, U31(U43(z0), x1)) -> c26(A__LENGTH(a__U31(a__U43(mark(z0)), x1)), MARK(U31(U43(z0), x1))) A__U61(tt, U31(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatIList(z0), x1)), MARK(U31(isNatIList(z0), x1))) A__U61(tt, U31(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U31(a__U51(mark(z0), z1, z2), x1)), MARK(U31(U51(z0, z1, z2), x1))) A__U61(tt, U31(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U52(mark(z0), z1), x1)), MARK(U31(U52(z0, z1), x1))) A__U61(tt, U31(U53(z0), x1)) -> c26(A__LENGTH(a__U31(a__U53(mark(z0)), x1)), MARK(U31(U53(z0), x1))) A__U61(tt, U31(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U61(mark(z0), z1), x1)), MARK(U31(U61(z0, z1), x1))) A__U61(tt, U31(length(z0), x1)) -> c26(A__LENGTH(a__U31(a__length(mark(z0)), x1)), MARK(U31(length(z0), x1))) A__U61(tt, U31(and(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__and(mark(z0), z1), x1)), MARK(U31(and(z0, z1), x1))) A__U61(tt, U31(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatIListKind(z0), x1)), MARK(U31(isNatIListKind(z0), x1))) A__U61(tt, U31(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatKind(z0), x1)), MARK(U31(isNatKind(z0), x1))) A__U61(tt, U31(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U31(cons(mark(z0), z1), x1)), MARK(U31(cons(z0, z1), x1))) A__U61(tt, U31(tt, x1)) -> c26(A__LENGTH(a__U31(tt, x1)), MARK(U31(tt, x1))) A__U61(tt, U31(s(z0), x1)) -> c26(A__LENGTH(a__U31(s(mark(z0)), x1)), MARK(U31(s(z0), x1))) A__U61(tt, U31(x0, z1)) -> c26(MARK(U31(x0, z1))) A__U61(tt, U31(0, x1)) -> c26(A__LENGTH(a__U31(0, x1))) A__U61(tt, U31(nil, x1)) -> c26(A__LENGTH(a__U31(nil, x1))) A__U61(tt, U32(zeros)) -> c26(A__LENGTH(a__U32(a__zeros)), MARK(U32(zeros))) A__U61(tt, U32(U11(z0, z1))) -> c26(A__LENGTH(a__U32(a__U11(mark(z0), z1))), MARK(U32(U11(z0, z1)))) A__U61(tt, U32(U12(z0))) -> c26(A__LENGTH(a__U32(a__U12(mark(z0)))), MARK(U32(U12(z0)))) A__U61(tt, U32(isNatList(z0))) -> c26(A__LENGTH(a__U32(a__isNatList(z0))), MARK(U32(isNatList(z0)))) A__U61(tt, U32(U21(z0, z1))) -> c26(A__LENGTH(a__U32(a__U21(mark(z0), z1))), MARK(U32(U21(z0, z1)))) A__U61(tt, U32(U22(z0))) -> c26(A__LENGTH(a__U32(a__U22(mark(z0)))), MARK(U32(U22(z0)))) A__U61(tt, U32(isNat(z0))) -> c26(A__LENGTH(a__U32(a__isNat(z0))), MARK(U32(isNat(z0)))) A__U61(tt, U32(U31(z0, z1))) -> c26(A__LENGTH(a__U32(a__U31(mark(z0), z1))), MARK(U32(U31(z0, z1)))) A__U61(tt, U32(U32(z0))) -> c26(A__LENGTH(a__U32(a__U32(mark(z0)))), MARK(U32(U32(z0)))) A__U61(tt, U32(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U32(a__U41(mark(z0), z1, z2))), MARK(U32(U41(z0, z1, z2)))) A__U61(tt, U32(U42(z0, z1))) -> c26(A__LENGTH(a__U32(a__U42(mark(z0), z1))), MARK(U32(U42(z0, z1)))) A__U61(tt, U32(U43(z0))) -> c26(A__LENGTH(a__U32(a__U43(mark(z0)))), MARK(U32(U43(z0)))) A__U61(tt, U32(isNatIList(z0))) -> c26(A__LENGTH(a__U32(a__isNatIList(z0))), MARK(U32(isNatIList(z0)))) A__U61(tt, U32(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U32(a__U51(mark(z0), z1, z2))), MARK(U32(U51(z0, z1, z2)))) A__U61(tt, U32(U52(z0, z1))) -> c26(A__LENGTH(a__U32(a__U52(mark(z0), z1))), MARK(U32(U52(z0, z1)))) A__U61(tt, U32(U53(z0))) -> c26(A__LENGTH(a__U32(a__U53(mark(z0)))), MARK(U32(U53(z0)))) A__U61(tt, U32(U61(z0, z1))) -> c26(A__LENGTH(a__U32(a__U61(mark(z0), z1))), MARK(U32(U61(z0, z1)))) A__U61(tt, U32(length(z0))) -> c26(A__LENGTH(a__U32(a__length(mark(z0)))), MARK(U32(length(z0)))) A__U61(tt, U32(and(z0, z1))) -> c26(A__LENGTH(a__U32(a__and(mark(z0), z1))), MARK(U32(and(z0, z1)))) A__U61(tt, U32(isNatIListKind(z0))) -> c26(A__LENGTH(a__U32(a__isNatIListKind(z0))), MARK(U32(isNatIListKind(z0)))) A__U61(tt, U32(isNatKind(z0))) -> c26(A__LENGTH(a__U32(a__isNatKind(z0))), MARK(U32(isNatKind(z0)))) A__U61(tt, U32(cons(z0, z1))) -> c26(A__LENGTH(a__U32(cons(mark(z0), z1))), MARK(U32(cons(z0, z1)))) A__U61(tt, U32(0)) -> c26(A__LENGTH(a__U32(0)), MARK(U32(0))) A__U61(tt, U32(tt)) -> c26(A__LENGTH(a__U32(tt)), MARK(U32(tt))) A__U61(tt, U32(s(z0))) -> c26(A__LENGTH(a__U32(s(mark(z0)))), MARK(U32(s(z0)))) A__U61(tt, U32(nil)) -> c26(A__LENGTH(a__U32(nil)), MARK(U32(nil))) A__U61(tt, U32(x0)) -> c26(MARK(U32(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_1, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c14_2, c20_2 ---------------------------------------- (179) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U61(tt, U41(z0, z1, z2)) -> c26(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) by A__U61(tt, U41(x0, z1, z2)) -> c26(A__LENGTH(U41(mark(x0), z1, z2)), MARK(U41(x0, z1, z2))) A__U61(tt, U41(zeros, x1, x2)) -> c26(A__LENGTH(a__U41(a__zeros, x1, x2)), MARK(U41(zeros, x1, x2))) A__U61(tt, U41(U11(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(U41(U11(z0, z1), x1, x2))) A__U61(tt, U41(U12(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U12(mark(z0)), x1, x2)), MARK(U41(U12(z0), x1, x2))) A__U61(tt, U41(isNatList(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatList(z0), x1, x2)), MARK(U41(isNatList(z0), x1, x2))) A__U61(tt, U41(U21(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(U41(U21(z0, z1), x1, x2))) A__U61(tt, U41(U22(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U22(mark(z0)), x1, x2)), MARK(U41(U22(z0), x1, x2))) A__U61(tt, U41(isNat(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNat(z0), x1, x2)), MARK(U41(isNat(z0), x1, x2))) A__U61(tt, U41(U31(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(U41(U31(z0, z1), x1, x2))) A__U61(tt, U41(U32(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U32(mark(z0)), x1, x2)), MARK(U41(U32(z0), x1, x2))) A__U61(tt, U41(U41(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2))) A__U61(tt, U41(U42(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U42(mark(z0), z1), x1, x2)), MARK(U41(U42(z0, z1), x1, x2))) A__U61(tt, U41(U43(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U43(mark(z0)), x1, x2)), MARK(U41(U43(z0), x1, x2))) A__U61(tt, U41(isNatIList(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatIList(z0), x1, x2)), MARK(U41(isNatIList(z0), x1, x2))) A__U61(tt, U41(U51(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U41(a__U51(mark(z0), z1, z2), x1, x2)), MARK(U41(U51(z0, z1, z2), x1, x2))) A__U61(tt, U41(U52(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U52(mark(z0), z1), x1, x2)), MARK(U41(U52(z0, z1), x1, x2))) A__U61(tt, U41(U53(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U53(mark(z0)), x1, x2)), MARK(U41(U53(z0), x1, x2))) A__U61(tt, U41(U61(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U61(mark(z0), z1), x1, x2)), MARK(U41(U61(z0, z1), x1, x2))) A__U61(tt, U41(length(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__length(mark(z0)), x1, x2)), MARK(U41(length(z0), x1, x2))) A__U61(tt, U41(and(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__and(mark(z0), z1), x1, x2)), MARK(U41(and(z0, z1), x1, x2))) A__U61(tt, U41(isNatIListKind(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatIListKind(z0), x1, x2)), MARK(U41(isNatIListKind(z0), x1, x2))) A__U61(tt, U41(isNatKind(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatKind(z0), x1, x2)), MARK(U41(isNatKind(z0), x1, x2))) A__U61(tt, U41(cons(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(cons(mark(z0), z1), x1, x2)), MARK(U41(cons(z0, z1), x1, x2))) A__U61(tt, U41(0, x1, x2)) -> c26(A__LENGTH(a__U41(0, x1, x2)), MARK(U41(0, x1, x2))) A__U61(tt, U41(tt, x1, x2)) -> c26(A__LENGTH(a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2))) A__U61(tt, U41(s(z0), x1, x2)) -> c26(A__LENGTH(a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2))) A__U61(tt, U41(nil, x1, x2)) -> c26(A__LENGTH(a__U41(nil, x1, x2)), MARK(U41(nil, x1, x2))) ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), 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MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, 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MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> c26(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U61(tt, U12(U21(z0, z1))) -> c26(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U61(tt, U12(U22(z0))) -> c26(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U61(tt, U12(isNat(z0))) -> c26(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U61(tt, U12(U31(z0, z1))) -> c26(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U61(tt, U12(U32(z0))) -> c26(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U61(tt, U12(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U61(tt, U12(U42(z0, z1))) -> c26(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U61(tt, U12(U43(z0))) -> c26(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U61(tt, U12(isNatIList(z0))) -> c26(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U61(tt, U12(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U61(tt, U12(U52(z0, z1))) -> c26(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U61(tt, U12(U53(z0))) -> c26(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U61(tt, U12(U61(z0, z1))) -> c26(A__LENGTH(a__U12(a__U61(mark(z0), z1))), MARK(U12(U61(z0, z1)))) A__U61(tt, U12(length(z0))) -> c26(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U61(tt, U12(and(z0, z1))) -> c26(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U61(tt, U12(isNatIListKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U61(tt, U12(isNatKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U61(tt, U12(cons(z0, z1))) -> c26(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U61(tt, U12(0)) -> c26(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U61(tt, U12(tt)) -> c26(A__LENGTH(a__U12(tt)), MARK(U12(tt))) A__U61(tt, U12(s(z0))) -> c26(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U61(tt, U12(nil)) -> c26(A__LENGTH(a__U12(nil)), MARK(U12(nil))) A__U61(tt, U12(x0)) -> c26(MARK(U12(x0))) A__U61(tt, isNatList(cons(z0, z1))) -> c26(A__LENGTH(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(cons(z0, z1)))) A__U61(tt, isNatList(nil)) -> c26(MARK(isNatList(nil))) A__U61(tt, isNatList(z0)) -> c26(MARK(isNatList(z0))) A__U61(tt, U21(zeros, x1)) -> c26(A__LENGTH(a__U21(a__zeros, x1)), MARK(U21(zeros, x1))) A__U61(tt, U21(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1)), MARK(U21(U11(z0, z1), x1))) A__U61(tt, U21(U12(z0), x1)) -> c26(A__LENGTH(a__U21(a__U12(mark(z0)), x1)), MARK(U21(U12(z0), x1))) A__U61(tt, U21(isNatList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatList(z0), x1)), MARK(U21(isNatList(z0), x1))) A__U61(tt, U21(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U21(mark(z0), z1), x1)), MARK(U21(U21(z0, z1), x1))) A__U61(tt, U21(U22(z0), x1)) -> c26(A__LENGTH(a__U21(a__U22(mark(z0)), x1)), MARK(U21(U22(z0), x1))) A__U61(tt, U21(isNat(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNat(z0), x1)), MARK(U21(isNat(z0), x1))) A__U61(tt, U21(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U31(mark(z0), z1), x1)), MARK(U21(U31(z0, z1), x1))) A__U61(tt, U21(U32(z0), x1)) -> c26(A__LENGTH(a__U21(a__U32(mark(z0)), x1)), MARK(U21(U32(z0), x1))) A__U61(tt, U21(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(U21(U41(z0, z1, z2), x1))) A__U61(tt, U21(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U42(mark(z0), z1), x1)), MARK(U21(U42(z0, z1), x1))) A__U61(tt, U21(U43(z0), x1)) -> c26(A__LENGTH(a__U21(a__U43(mark(z0)), x1)), MARK(U21(U43(z0), x1))) A__U61(tt, U21(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIList(z0), x1)), MARK(U21(isNatIList(z0), x1))) A__U61(tt, U21(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U51(mark(z0), z1, z2), x1)), MARK(U21(U51(z0, z1, z2), x1))) A__U61(tt, U21(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U52(mark(z0), z1), x1)), MARK(U21(U52(z0, z1), x1))) A__U61(tt, U21(U53(z0), x1)) -> c26(A__LENGTH(a__U21(a__U53(mark(z0)), x1)), MARK(U21(U53(z0), x1))) A__U61(tt, U21(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U61(mark(z0), z1), x1)), MARK(U21(U61(z0, z1), x1))) A__U61(tt, U21(length(z0), x1)) -> c26(A__LENGTH(a__U21(a__length(mark(z0)), x1)), MARK(U21(length(z0), x1))) A__U61(tt, U21(and(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__and(mark(z0), z1), x1)), MARK(U21(and(z0, z1), x1))) A__U61(tt, U21(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIListKind(z0), x1)), MARK(U21(isNatIListKind(z0), x1))) A__U61(tt, U21(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), x1)), MARK(U21(isNatKind(z0), x1))) A__U61(tt, U21(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U21(cons(mark(z0), z1), x1)), MARK(U21(cons(z0, z1), x1))) A__U61(tt, U21(tt, x1)) -> c26(A__LENGTH(a__U21(tt, x1)), MARK(U21(tt, x1))) A__U61(tt, U21(s(z0), x1)) -> c26(A__LENGTH(a__U21(s(mark(z0)), x1)), MARK(U21(s(z0), x1))) A__U61(tt, U21(x0, z1)) -> c26(MARK(U21(x0, z1))) A__U61(tt, U21(0, x1)) -> c26(A__LENGTH(a__U21(0, x1))) A__U61(tt, U21(nil, x1)) -> c26(A__LENGTH(a__U21(nil, x1))) A__U61(tt, U22(zeros)) -> c26(A__LENGTH(a__U22(a__zeros)), MARK(U22(zeros))) A__U61(tt, U22(U11(z0, z1))) -> c26(A__LENGTH(a__U22(a__U11(mark(z0), z1))), MARK(U22(U11(z0, z1)))) A__U61(tt, U22(U12(z0))) -> c26(A__LENGTH(a__U22(a__U12(mark(z0)))), MARK(U22(U12(z0)))) A__U61(tt, U22(isNatList(z0))) -> c26(A__LENGTH(a__U22(a__isNatList(z0))), MARK(U22(isNatList(z0)))) A__U61(tt, U22(U21(z0, z1))) -> c26(A__LENGTH(a__U22(a__U21(mark(z0), z1))), MARK(U22(U21(z0, z1)))) A__U61(tt, U22(U22(z0))) -> c26(A__LENGTH(a__U22(a__U22(mark(z0)))), MARK(U22(U22(z0)))) A__U61(tt, U22(isNat(z0))) -> c26(A__LENGTH(a__U22(a__isNat(z0))), MARK(U22(isNat(z0)))) A__U61(tt, U22(U31(z0, z1))) -> c26(A__LENGTH(a__U22(a__U31(mark(z0), z1))), MARK(U22(U31(z0, z1)))) A__U61(tt, U22(U32(z0))) -> c26(A__LENGTH(a__U22(a__U32(mark(z0)))), MARK(U22(U32(z0)))) A__U61(tt, U22(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U22(a__U41(mark(z0), z1, z2))), MARK(U22(U41(z0, z1, z2)))) A__U61(tt, U22(U42(z0, z1))) -> c26(A__LENGTH(a__U22(a__U42(mark(z0), z1))), MARK(U22(U42(z0, z1)))) A__U61(tt, U22(U43(z0))) -> c26(A__LENGTH(a__U22(a__U43(mark(z0)))), MARK(U22(U43(z0)))) A__U61(tt, U22(isNatIList(z0))) -> c26(A__LENGTH(a__U22(a__isNatIList(z0))), MARK(U22(isNatIList(z0)))) A__U61(tt, U22(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U22(a__U51(mark(z0), z1, z2))), MARK(U22(U51(z0, z1, z2)))) A__U61(tt, U22(U52(z0, z1))) -> c26(A__LENGTH(a__U22(a__U52(mark(z0), z1))), MARK(U22(U52(z0, z1)))) A__U61(tt, U22(U53(z0))) -> c26(A__LENGTH(a__U22(a__U53(mark(z0)))), MARK(U22(U53(z0)))) A__U61(tt, U22(U61(z0, z1))) -> c26(A__LENGTH(a__U22(a__U61(mark(z0), z1))), MARK(U22(U61(z0, z1)))) A__U61(tt, U22(length(z0))) -> c26(A__LENGTH(a__U22(a__length(mark(z0)))), MARK(U22(length(z0)))) A__U61(tt, U22(and(z0, z1))) -> c26(A__LENGTH(a__U22(a__and(mark(z0), z1))), MARK(U22(and(z0, z1)))) A__U61(tt, U22(isNatIListKind(z0))) -> c26(A__LENGTH(a__U22(a__isNatIListKind(z0))), MARK(U22(isNatIListKind(z0)))) A__U61(tt, U22(isNatKind(z0))) -> c26(A__LENGTH(a__U22(a__isNatKind(z0))), MARK(U22(isNatKind(z0)))) A__U61(tt, U22(cons(z0, z1))) -> c26(A__LENGTH(a__U22(cons(mark(z0), z1))), MARK(U22(cons(z0, z1)))) A__U61(tt, U22(0)) -> c26(A__LENGTH(a__U22(0)), MARK(U22(0))) A__U61(tt, U22(tt)) -> c26(A__LENGTH(a__U22(tt)), MARK(U22(tt))) A__U61(tt, U22(s(z0))) -> c26(A__LENGTH(a__U22(s(mark(z0)))), MARK(U22(s(z0)))) A__U61(tt, U22(nil)) -> c26(A__LENGTH(a__U22(nil)), MARK(U22(nil))) A__U61(tt, U22(x0)) -> c26(MARK(U22(x0))) A__U61(tt, isNat(length(z0))) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), z0)), MARK(isNat(length(z0)))) A__U61(tt, isNat(s(z0))) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), z0)), MARK(isNat(s(z0)))) A__U61(tt, isNat(0)) -> c26(MARK(isNat(0))) A__U61(tt, isNat(z0)) -> c26(MARK(isNat(z0))) A__U61(tt, U31(zeros, x1)) -> c26(A__LENGTH(a__U31(a__zeros, x1)), MARK(U31(zeros, x1))) A__U61(tt, U31(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U11(mark(z0), z1), x1)), MARK(U31(U11(z0, z1), x1))) A__U61(tt, U31(U12(z0), x1)) -> c26(A__LENGTH(a__U31(a__U12(mark(z0)), x1)), MARK(U31(U12(z0), x1))) A__U61(tt, U31(isNatList(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatList(z0), x1)), MARK(U31(isNatList(z0), x1))) A__U61(tt, U31(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U21(mark(z0), z1), x1)), MARK(U31(U21(z0, z1), x1))) A__U61(tt, U31(U22(z0), x1)) -> c26(A__LENGTH(a__U31(a__U22(mark(z0)), x1)), MARK(U31(U22(z0), x1))) A__U61(tt, U31(isNat(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNat(z0), x1)), MARK(U31(isNat(z0), x1))) A__U61(tt, U31(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U31(mark(z0), z1), x1)), MARK(U31(U31(z0, z1), x1))) A__U61(tt, U31(U32(z0), x1)) -> c26(A__LENGTH(a__U31(a__U32(mark(z0)), x1)), MARK(U31(U32(z0), x1))) A__U61(tt, U31(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(U31(U41(z0, z1, z2), x1))) A__U61(tt, U31(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U42(mark(z0), z1), x1)), MARK(U31(U42(z0, z1), x1))) A__U61(tt, U31(U43(z0), x1)) -> c26(A__LENGTH(a__U31(a__U43(mark(z0)), x1)), MARK(U31(U43(z0), x1))) A__U61(tt, U31(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatIList(z0), x1)), MARK(U31(isNatIList(z0), x1))) A__U61(tt, U31(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U31(a__U51(mark(z0), z1, z2), x1)), MARK(U31(U51(z0, z1, z2), x1))) A__U61(tt, U31(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U52(mark(z0), z1), x1)), MARK(U31(U52(z0, z1), x1))) A__U61(tt, U31(U53(z0), x1)) -> c26(A__LENGTH(a__U31(a__U53(mark(z0)), x1)), MARK(U31(U53(z0), x1))) A__U61(tt, U31(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U61(mark(z0), z1), x1)), MARK(U31(U61(z0, z1), x1))) A__U61(tt, U31(length(z0), x1)) -> c26(A__LENGTH(a__U31(a__length(mark(z0)), x1)), MARK(U31(length(z0), x1))) A__U61(tt, U31(and(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__and(mark(z0), z1), x1)), MARK(U31(and(z0, z1), x1))) A__U61(tt, U31(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatIListKind(z0), x1)), MARK(U31(isNatIListKind(z0), x1))) A__U61(tt, U31(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatKind(z0), x1)), MARK(U31(isNatKind(z0), x1))) A__U61(tt, U31(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U31(cons(mark(z0), z1), x1)), MARK(U31(cons(z0, z1), x1))) A__U61(tt, U31(tt, x1)) -> c26(A__LENGTH(a__U31(tt, x1)), MARK(U31(tt, x1))) A__U61(tt, U31(s(z0), x1)) -> c26(A__LENGTH(a__U31(s(mark(z0)), x1)), MARK(U31(s(z0), x1))) A__U61(tt, U31(x0, z1)) -> c26(MARK(U31(x0, z1))) A__U61(tt, U31(0, x1)) -> c26(A__LENGTH(a__U31(0, x1))) A__U61(tt, U31(nil, x1)) -> c26(A__LENGTH(a__U31(nil, x1))) A__U61(tt, U32(zeros)) -> c26(A__LENGTH(a__U32(a__zeros)), MARK(U32(zeros))) A__U61(tt, U32(U11(z0, z1))) -> c26(A__LENGTH(a__U32(a__U11(mark(z0), z1))), MARK(U32(U11(z0, z1)))) A__U61(tt, U32(U12(z0))) -> c26(A__LENGTH(a__U32(a__U12(mark(z0)))), MARK(U32(U12(z0)))) A__U61(tt, U32(isNatList(z0))) -> c26(A__LENGTH(a__U32(a__isNatList(z0))), MARK(U32(isNatList(z0)))) A__U61(tt, U32(U21(z0, z1))) -> c26(A__LENGTH(a__U32(a__U21(mark(z0), z1))), MARK(U32(U21(z0, z1)))) A__U61(tt, U32(U22(z0))) -> c26(A__LENGTH(a__U32(a__U22(mark(z0)))), MARK(U32(U22(z0)))) A__U61(tt, U32(isNat(z0))) -> c26(A__LENGTH(a__U32(a__isNat(z0))), MARK(U32(isNat(z0)))) A__U61(tt, U32(U31(z0, z1))) -> c26(A__LENGTH(a__U32(a__U31(mark(z0), z1))), MARK(U32(U31(z0, z1)))) A__U61(tt, U32(U32(z0))) -> c26(A__LENGTH(a__U32(a__U32(mark(z0)))), MARK(U32(U32(z0)))) A__U61(tt, U32(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U32(a__U41(mark(z0), z1, z2))), MARK(U32(U41(z0, z1, z2)))) A__U61(tt, U32(U42(z0, z1))) -> c26(A__LENGTH(a__U32(a__U42(mark(z0), z1))), MARK(U32(U42(z0, z1)))) A__U61(tt, U32(U43(z0))) -> c26(A__LENGTH(a__U32(a__U43(mark(z0)))), MARK(U32(U43(z0)))) A__U61(tt, U32(isNatIList(z0))) -> c26(A__LENGTH(a__U32(a__isNatIList(z0))), MARK(U32(isNatIList(z0)))) A__U61(tt, U32(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U32(a__U51(mark(z0), z1, z2))), MARK(U32(U51(z0, z1, z2)))) A__U61(tt, U32(U52(z0, z1))) -> c26(A__LENGTH(a__U32(a__U52(mark(z0), z1))), MARK(U32(U52(z0, z1)))) A__U61(tt, U32(U53(z0))) -> c26(A__LENGTH(a__U32(a__U53(mark(z0)))), MARK(U32(U53(z0)))) A__U61(tt, U32(U61(z0, z1))) -> c26(A__LENGTH(a__U32(a__U61(mark(z0), z1))), MARK(U32(U61(z0, z1)))) A__U61(tt, U32(length(z0))) -> c26(A__LENGTH(a__U32(a__length(mark(z0)))), MARK(U32(length(z0)))) A__U61(tt, U32(and(z0, z1))) -> c26(A__LENGTH(a__U32(a__and(mark(z0), z1))), MARK(U32(and(z0, z1)))) A__U61(tt, U32(isNatIListKind(z0))) -> c26(A__LENGTH(a__U32(a__isNatIListKind(z0))), MARK(U32(isNatIListKind(z0)))) A__U61(tt, U32(isNatKind(z0))) -> c26(A__LENGTH(a__U32(a__isNatKind(z0))), MARK(U32(isNatKind(z0)))) A__U61(tt, U32(cons(z0, z1))) -> c26(A__LENGTH(a__U32(cons(mark(z0), z1))), MARK(U32(cons(z0, z1)))) A__U61(tt, U32(0)) -> c26(A__LENGTH(a__U32(0)), MARK(U32(0))) A__U61(tt, U32(tt)) -> c26(A__LENGTH(a__U32(tt)), MARK(U32(tt))) A__U61(tt, U32(s(z0))) -> c26(A__LENGTH(a__U32(s(mark(z0)))), MARK(U32(s(z0)))) A__U61(tt, U32(nil)) -> c26(A__LENGTH(a__U32(nil)), MARK(U32(nil))) A__U61(tt, U32(x0)) -> c26(MARK(U32(x0))) A__U61(tt, U41(x0, z1, z2)) -> c26(A__LENGTH(U41(mark(x0), z1, z2)), MARK(U41(x0, z1, z2))) A__U61(tt, U41(zeros, x1, x2)) -> c26(A__LENGTH(a__U41(a__zeros, x1, x2)), MARK(U41(zeros, x1, x2))) A__U61(tt, U41(U11(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(U41(U11(z0, z1), x1, x2))) A__U61(tt, U41(U12(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U12(mark(z0)), x1, x2)), MARK(U41(U12(z0), x1, x2))) A__U61(tt, U41(isNatList(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatList(z0), x1, x2)), MARK(U41(isNatList(z0), x1, x2))) A__U61(tt, U41(U21(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(U41(U21(z0, z1), x1, x2))) A__U61(tt, U41(U22(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U22(mark(z0)), x1, x2)), MARK(U41(U22(z0), x1, x2))) A__U61(tt, U41(isNat(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNat(z0), x1, x2)), MARK(U41(isNat(z0), x1, x2))) A__U61(tt, U41(U31(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(U41(U31(z0, z1), x1, x2))) A__U61(tt, U41(U32(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U32(mark(z0)), x1, x2)), MARK(U41(U32(z0), x1, x2))) A__U61(tt, U41(U41(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2))) A__U61(tt, U41(U42(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U42(mark(z0), z1), x1, x2)), MARK(U41(U42(z0, z1), x1, x2))) A__U61(tt, U41(U43(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U43(mark(z0)), x1, x2)), MARK(U41(U43(z0), x1, x2))) A__U61(tt, U41(isNatIList(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatIList(z0), x1, x2)), MARK(U41(isNatIList(z0), x1, x2))) A__U61(tt, U41(U51(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U41(a__U51(mark(z0), z1, z2), x1, x2)), MARK(U41(U51(z0, z1, z2), x1, x2))) A__U61(tt, U41(U52(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U52(mark(z0), z1), x1, x2)), MARK(U41(U52(z0, z1), x1, x2))) A__U61(tt, U41(U53(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U53(mark(z0)), x1, x2)), MARK(U41(U53(z0), x1, x2))) A__U61(tt, U41(U61(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U61(mark(z0), z1), x1, x2)), MARK(U41(U61(z0, z1), x1, x2))) A__U61(tt, U41(length(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__length(mark(z0)), x1, x2)), MARK(U41(length(z0), x1, x2))) A__U61(tt, U41(and(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__and(mark(z0), z1), x1, x2)), MARK(U41(and(z0, z1), x1, x2))) A__U61(tt, U41(isNatIListKind(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatIListKind(z0), x1, x2)), MARK(U41(isNatIListKind(z0), x1, x2))) A__U61(tt, U41(isNatKind(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatKind(z0), x1, x2)), MARK(U41(isNatKind(z0), x1, x2))) A__U61(tt, U41(cons(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(cons(mark(z0), z1), x1, x2)), MARK(U41(cons(z0, z1), x1, x2))) A__U61(tt, U41(0, x1, x2)) -> c26(A__LENGTH(a__U41(0, x1, x2)), MARK(U41(0, x1, x2))) A__U61(tt, U41(tt, x1, x2)) -> c26(A__LENGTH(a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2))) A__U61(tt, U41(s(z0), x1, x2)) -> c26(A__LENGTH(a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2))) A__U61(tt, U41(nil, x1, x2)) -> c26(A__LENGTH(a__U41(nil, x1, x2)), MARK(U41(nil, x1, x2))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), 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c26(A__LENGTH(a__U21(nil, x1))) A__U61(tt, U22(zeros)) -> c26(A__LENGTH(a__U22(a__zeros)), MARK(U22(zeros))) A__U61(tt, U22(U11(z0, z1))) -> c26(A__LENGTH(a__U22(a__U11(mark(z0), z1))), MARK(U22(U11(z0, z1)))) A__U61(tt, U22(U12(z0))) -> c26(A__LENGTH(a__U22(a__U12(mark(z0)))), MARK(U22(U12(z0)))) A__U61(tt, U22(isNatList(z0))) -> c26(A__LENGTH(a__U22(a__isNatList(z0))), MARK(U22(isNatList(z0)))) A__U61(tt, U22(U21(z0, z1))) -> c26(A__LENGTH(a__U22(a__U21(mark(z0), z1))), MARK(U22(U21(z0, z1)))) A__U61(tt, U22(U22(z0))) -> c26(A__LENGTH(a__U22(a__U22(mark(z0)))), MARK(U22(U22(z0)))) A__U61(tt, U22(isNat(z0))) -> c26(A__LENGTH(a__U22(a__isNat(z0))), MARK(U22(isNat(z0)))) A__U61(tt, U22(U31(z0, z1))) -> c26(A__LENGTH(a__U22(a__U31(mark(z0), z1))), MARK(U22(U31(z0, z1)))) A__U61(tt, U22(U32(z0))) -> c26(A__LENGTH(a__U22(a__U32(mark(z0)))), MARK(U22(U32(z0)))) A__U61(tt, U22(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U22(a__U41(mark(z0), z1, z2))), MARK(U22(U41(z0, z1, z2)))) A__U61(tt, U22(U42(z0, z1))) -> c26(A__LENGTH(a__U22(a__U42(mark(z0), z1))), MARK(U22(U42(z0, z1)))) A__U61(tt, U22(U43(z0))) -> c26(A__LENGTH(a__U22(a__U43(mark(z0)))), MARK(U22(U43(z0)))) A__U61(tt, U22(isNatIList(z0))) -> c26(A__LENGTH(a__U22(a__isNatIList(z0))), MARK(U22(isNatIList(z0)))) A__U61(tt, U22(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U22(a__U51(mark(z0), z1, z2))), MARK(U22(U51(z0, z1, z2)))) A__U61(tt, U22(U52(z0, z1))) -> c26(A__LENGTH(a__U22(a__U52(mark(z0), z1))), MARK(U22(U52(z0, z1)))) A__U61(tt, U22(U53(z0))) -> c26(A__LENGTH(a__U22(a__U53(mark(z0)))), MARK(U22(U53(z0)))) A__U61(tt, U22(U61(z0, z1))) -> c26(A__LENGTH(a__U22(a__U61(mark(z0), z1))), MARK(U22(U61(z0, z1)))) A__U61(tt, U22(length(z0))) -> c26(A__LENGTH(a__U22(a__length(mark(z0)))), MARK(U22(length(z0)))) A__U61(tt, U22(and(z0, z1))) -> c26(A__LENGTH(a__U22(a__and(mark(z0), z1))), MARK(U22(and(z0, z1)))) A__U61(tt, U22(isNatIListKind(z0))) -> c26(A__LENGTH(a__U22(a__isNatIListKind(z0))), MARK(U22(isNatIListKind(z0)))) A__U61(tt, U22(isNatKind(z0))) -> c26(A__LENGTH(a__U22(a__isNatKind(z0))), MARK(U22(isNatKind(z0)))) A__U61(tt, U22(cons(z0, z1))) -> c26(A__LENGTH(a__U22(cons(mark(z0), z1))), MARK(U22(cons(z0, z1)))) A__U61(tt, U22(0)) -> c26(A__LENGTH(a__U22(0)), MARK(U22(0))) A__U61(tt, U22(tt)) -> c26(A__LENGTH(a__U22(tt)), MARK(U22(tt))) A__U61(tt, U22(s(z0))) -> c26(A__LENGTH(a__U22(s(mark(z0)))), MARK(U22(s(z0)))) A__U61(tt, U22(nil)) -> c26(A__LENGTH(a__U22(nil)), MARK(U22(nil))) A__U61(tt, U22(x0)) -> c26(MARK(U22(x0))) A__U61(tt, isNat(length(z0))) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), z0)), MARK(isNat(length(z0)))) A__U61(tt, isNat(s(z0))) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), z0)), MARK(isNat(s(z0)))) A__U61(tt, isNat(0)) -> c26(MARK(isNat(0))) A__U61(tt, isNat(z0)) -> c26(MARK(isNat(z0))) A__U61(tt, U31(zeros, x1)) -> c26(A__LENGTH(a__U31(a__zeros, x1)), MARK(U31(zeros, x1))) A__U61(tt, U31(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U11(mark(z0), z1), x1)), MARK(U31(U11(z0, z1), x1))) A__U61(tt, U31(U12(z0), x1)) -> c26(A__LENGTH(a__U31(a__U12(mark(z0)), x1)), MARK(U31(U12(z0), x1))) A__U61(tt, U31(isNatList(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatList(z0), x1)), MARK(U31(isNatList(z0), x1))) A__U61(tt, U31(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U21(mark(z0), z1), x1)), MARK(U31(U21(z0, z1), x1))) A__U61(tt, U31(U22(z0), x1)) -> c26(A__LENGTH(a__U31(a__U22(mark(z0)), x1)), MARK(U31(U22(z0), x1))) A__U61(tt, U31(isNat(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNat(z0), x1)), MARK(U31(isNat(z0), x1))) A__U61(tt, U31(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U31(mark(z0), z1), x1)), MARK(U31(U31(z0, z1), x1))) A__U61(tt, U31(U32(z0), x1)) -> c26(A__LENGTH(a__U31(a__U32(mark(z0)), x1)), MARK(U31(U32(z0), x1))) A__U61(tt, U31(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(U31(U41(z0, z1, z2), x1))) A__U61(tt, U31(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U42(mark(z0), z1), x1)), MARK(U31(U42(z0, z1), x1))) A__U61(tt, U31(U43(z0), x1)) -> c26(A__LENGTH(a__U31(a__U43(mark(z0)), x1)), MARK(U31(U43(z0), x1))) A__U61(tt, U31(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatIList(z0), x1)), MARK(U31(isNatIList(z0), x1))) A__U61(tt, U31(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U31(a__U51(mark(z0), z1, z2), x1)), MARK(U31(U51(z0, z1, z2), x1))) A__U61(tt, U31(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U52(mark(z0), z1), x1)), MARK(U31(U52(z0, z1), x1))) A__U61(tt, U31(U53(z0), x1)) -> c26(A__LENGTH(a__U31(a__U53(mark(z0)), x1)), MARK(U31(U53(z0), x1))) A__U61(tt, U31(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U61(mark(z0), z1), x1)), MARK(U31(U61(z0, z1), x1))) A__U61(tt, U31(length(z0), x1)) -> c26(A__LENGTH(a__U31(a__length(mark(z0)), x1)), MARK(U31(length(z0), x1))) A__U61(tt, U31(and(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__and(mark(z0), z1), x1)), MARK(U31(and(z0, z1), x1))) A__U61(tt, U31(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatIListKind(z0), x1)), MARK(U31(isNatIListKind(z0), x1))) A__U61(tt, U31(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatKind(z0), x1)), MARK(U31(isNatKind(z0), x1))) A__U61(tt, U31(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U31(cons(mark(z0), z1), x1)), MARK(U31(cons(z0, z1), x1))) A__U61(tt, U31(tt, x1)) -> c26(A__LENGTH(a__U31(tt, x1)), MARK(U31(tt, x1))) A__U61(tt, U31(s(z0), x1)) -> c26(A__LENGTH(a__U31(s(mark(z0)), x1)), MARK(U31(s(z0), x1))) A__U61(tt, U31(x0, z1)) -> c26(MARK(U31(x0, z1))) A__U61(tt, U31(0, x1)) -> c26(A__LENGTH(a__U31(0, x1))) A__U61(tt, U31(nil, x1)) -> c26(A__LENGTH(a__U31(nil, x1))) A__U61(tt, U32(zeros)) -> c26(A__LENGTH(a__U32(a__zeros)), MARK(U32(zeros))) A__U61(tt, U32(U11(z0, z1))) -> c26(A__LENGTH(a__U32(a__U11(mark(z0), z1))), MARK(U32(U11(z0, z1)))) A__U61(tt, U32(U12(z0))) -> c26(A__LENGTH(a__U32(a__U12(mark(z0)))), MARK(U32(U12(z0)))) A__U61(tt, U32(isNatList(z0))) -> c26(A__LENGTH(a__U32(a__isNatList(z0))), MARK(U32(isNatList(z0)))) A__U61(tt, U32(U21(z0, z1))) -> c26(A__LENGTH(a__U32(a__U21(mark(z0), z1))), MARK(U32(U21(z0, z1)))) A__U61(tt, U32(U22(z0))) -> c26(A__LENGTH(a__U32(a__U22(mark(z0)))), MARK(U32(U22(z0)))) A__U61(tt, U32(isNat(z0))) -> c26(A__LENGTH(a__U32(a__isNat(z0))), MARK(U32(isNat(z0)))) A__U61(tt, U32(U31(z0, z1))) -> c26(A__LENGTH(a__U32(a__U31(mark(z0), z1))), MARK(U32(U31(z0, z1)))) A__U61(tt, U32(U32(z0))) -> c26(A__LENGTH(a__U32(a__U32(mark(z0)))), MARK(U32(U32(z0)))) A__U61(tt, U32(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U32(a__U41(mark(z0), z1, z2))), MARK(U32(U41(z0, z1, z2)))) A__U61(tt, U32(U42(z0, z1))) -> c26(A__LENGTH(a__U32(a__U42(mark(z0), z1))), MARK(U32(U42(z0, z1)))) A__U61(tt, U32(U43(z0))) -> c26(A__LENGTH(a__U32(a__U43(mark(z0)))), MARK(U32(U43(z0)))) A__U61(tt, U32(isNatIList(z0))) -> c26(A__LENGTH(a__U32(a__isNatIList(z0))), MARK(U32(isNatIList(z0)))) A__U61(tt, U32(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U32(a__U51(mark(z0), z1, z2))), MARK(U32(U51(z0, z1, z2)))) A__U61(tt, U32(U52(z0, z1))) -> c26(A__LENGTH(a__U32(a__U52(mark(z0), z1))), MARK(U32(U52(z0, z1)))) A__U61(tt, U32(U53(z0))) -> c26(A__LENGTH(a__U32(a__U53(mark(z0)))), MARK(U32(U53(z0)))) A__U61(tt, U32(U61(z0, z1))) -> c26(A__LENGTH(a__U32(a__U61(mark(z0), z1))), MARK(U32(U61(z0, z1)))) A__U61(tt, U32(length(z0))) -> c26(A__LENGTH(a__U32(a__length(mark(z0)))), MARK(U32(length(z0)))) A__U61(tt, U32(and(z0, z1))) -> c26(A__LENGTH(a__U32(a__and(mark(z0), z1))), MARK(U32(and(z0, z1)))) A__U61(tt, U32(isNatIListKind(z0))) -> c26(A__LENGTH(a__U32(a__isNatIListKind(z0))), MARK(U32(isNatIListKind(z0)))) A__U61(tt, U32(isNatKind(z0))) -> c26(A__LENGTH(a__U32(a__isNatKind(z0))), MARK(U32(isNatKind(z0)))) A__U61(tt, U32(cons(z0, z1))) -> c26(A__LENGTH(a__U32(cons(mark(z0), z1))), MARK(U32(cons(z0, z1)))) A__U61(tt, U32(0)) -> c26(A__LENGTH(a__U32(0)), MARK(U32(0))) A__U61(tt, U32(tt)) -> c26(A__LENGTH(a__U32(tt)), MARK(U32(tt))) A__U61(tt, U32(s(z0))) -> c26(A__LENGTH(a__U32(s(mark(z0)))), MARK(U32(s(z0)))) A__U61(tt, U32(nil)) -> c26(A__LENGTH(a__U32(nil)), MARK(U32(nil))) A__U61(tt, U32(x0)) -> c26(MARK(U32(x0))) A__U61(tt, U41(x0, z1, z2)) -> c26(A__LENGTH(U41(mark(x0), z1, z2)), MARK(U41(x0, z1, z2))) A__U61(tt, U41(zeros, x1, x2)) -> c26(A__LENGTH(a__U41(a__zeros, x1, x2)), MARK(U41(zeros, x1, x2))) A__U61(tt, U41(U11(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(U41(U11(z0, z1), x1, x2))) A__U61(tt, U41(U12(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U12(mark(z0)), x1, x2)), MARK(U41(U12(z0), x1, x2))) A__U61(tt, U41(isNatList(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatList(z0), x1, x2)), MARK(U41(isNatList(z0), x1, x2))) A__U61(tt, U41(U21(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(U41(U21(z0, z1), x1, x2))) A__U61(tt, U41(U22(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U22(mark(z0)), x1, x2)), MARK(U41(U22(z0), x1, x2))) A__U61(tt, U41(isNat(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNat(z0), x1, x2)), MARK(U41(isNat(z0), x1, x2))) A__U61(tt, U41(U31(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(U41(U31(z0, z1), x1, x2))) A__U61(tt, U41(U32(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U32(mark(z0)), x1, x2)), MARK(U41(U32(z0), x1, x2))) A__U61(tt, U41(U41(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2))) A__U61(tt, U41(U42(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U42(mark(z0), z1), x1, x2)), MARK(U41(U42(z0, z1), x1, x2))) A__U61(tt, U41(U43(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U43(mark(z0)), x1, x2)), MARK(U41(U43(z0), x1, x2))) A__U61(tt, U41(isNatIList(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatIList(z0), x1, x2)), MARK(U41(isNatIList(z0), x1, x2))) A__U61(tt, U41(U51(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U41(a__U51(mark(z0), z1, z2), x1, x2)), MARK(U41(U51(z0, z1, z2), x1, x2))) A__U61(tt, U41(U52(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U52(mark(z0), z1), x1, x2)), MARK(U41(U52(z0, z1), x1, x2))) A__U61(tt, U41(U53(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U53(mark(z0)), x1, x2)), MARK(U41(U53(z0), x1, x2))) A__U61(tt, U41(U61(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U61(mark(z0), z1), x1, x2)), MARK(U41(U61(z0, z1), x1, x2))) A__U61(tt, U41(length(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__length(mark(z0)), x1, x2)), MARK(U41(length(z0), x1, x2))) A__U61(tt, U41(and(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__and(mark(z0), z1), x1, x2)), MARK(U41(and(z0, z1), x1, x2))) A__U61(tt, U41(isNatIListKind(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatIListKind(z0), x1, x2)), MARK(U41(isNatIListKind(z0), x1, x2))) A__U61(tt, U41(isNatKind(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatKind(z0), x1, x2)), MARK(U41(isNatKind(z0), x1, x2))) A__U61(tt, U41(cons(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(cons(mark(z0), z1), x1, x2)), MARK(U41(cons(z0, z1), x1, x2))) A__U61(tt, U41(0, x1, x2)) -> c26(A__LENGTH(a__U41(0, x1, x2)), MARK(U41(0, x1, x2))) A__U61(tt, U41(tt, x1, x2)) -> c26(A__LENGTH(a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2))) A__U61(tt, U41(s(z0), x1, x2)) -> c26(A__LENGTH(a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2))) A__U61(tt, U41(nil, x1, x2)) -> c26(A__LENGTH(a__U41(nil, x1, x2)), MARK(U41(nil, x1, 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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_1, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c14_2, c20_2 ---------------------------------------- (181) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> c26(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U61(tt, U12(U21(z0, z1))) -> c26(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U61(tt, U12(U22(z0))) -> c26(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U61(tt, U12(isNat(z0))) -> c26(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U61(tt, U12(U31(z0, z1))) -> c26(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U61(tt, U12(U32(z0))) -> c26(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U61(tt, U12(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U61(tt, U12(U42(z0, z1))) -> c26(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U61(tt, U12(U43(z0))) -> c26(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U61(tt, U12(isNatIList(z0))) -> c26(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U61(tt, U12(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U61(tt, U12(U52(z0, z1))) -> c26(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U61(tt, U12(U53(z0))) -> c26(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U61(tt, U12(U61(z0, z1))) -> c26(A__LENGTH(a__U12(a__U61(mark(z0), z1))), MARK(U12(U61(z0, z1)))) A__U61(tt, U12(length(z0))) -> c26(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U61(tt, U12(and(z0, z1))) -> c26(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U61(tt, U12(isNatIListKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U61(tt, U12(isNatKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U61(tt, U12(cons(z0, z1))) -> c26(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U61(tt, U12(0)) -> c26(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U61(tt, U12(tt)) -> c26(A__LENGTH(a__U12(tt)), MARK(U12(tt))) A__U61(tt, U12(s(z0))) -> c26(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U61(tt, U12(nil)) -> c26(A__LENGTH(a__U12(nil)), MARK(U12(nil))) A__U61(tt, U12(x0)) -> c26(MARK(U12(x0))) A__U61(tt, isNatList(cons(z0, z1))) -> c26(A__LENGTH(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(cons(z0, z1)))) A__U61(tt, isNatList(nil)) -> c26(MARK(isNatList(nil))) A__U61(tt, isNatList(z0)) -> c26(MARK(isNatList(z0))) A__U61(tt, U21(zeros, x1)) -> c26(A__LENGTH(a__U21(a__zeros, x1)), MARK(U21(zeros, x1))) A__U61(tt, U21(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1)), MARK(U21(U11(z0, z1), x1))) A__U61(tt, U21(U12(z0), x1)) -> c26(A__LENGTH(a__U21(a__U12(mark(z0)), x1)), MARK(U21(U12(z0), x1))) A__U61(tt, U21(isNatList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatList(z0), x1)), MARK(U21(isNatList(z0), x1))) A__U61(tt, U21(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U21(mark(z0), z1), x1)), MARK(U21(U21(z0, z1), x1))) A__U61(tt, U21(U22(z0), x1)) -> c26(A__LENGTH(a__U21(a__U22(mark(z0)), x1)), MARK(U21(U22(z0), x1))) A__U61(tt, U21(isNat(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNat(z0), x1)), MARK(U21(isNat(z0), x1))) A__U61(tt, U21(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U31(mark(z0), z1), x1)), MARK(U21(U31(z0, z1), x1))) A__U61(tt, U21(U32(z0), x1)) -> c26(A__LENGTH(a__U21(a__U32(mark(z0)), x1)), MARK(U21(U32(z0), x1))) A__U61(tt, U21(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(U21(U41(z0, z1, z2), x1))) A__U61(tt, U21(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U42(mark(z0), z1), x1)), MARK(U21(U42(z0, z1), x1))) A__U61(tt, U21(U43(z0), x1)) -> c26(A__LENGTH(a__U21(a__U43(mark(z0)), x1)), MARK(U21(U43(z0), x1))) A__U61(tt, U21(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIList(z0), x1)), MARK(U21(isNatIList(z0), x1))) A__U61(tt, U21(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U51(mark(z0), z1, z2), x1)), MARK(U21(U51(z0, z1, z2), x1))) A__U61(tt, U21(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U52(mark(z0), z1), x1)), MARK(U21(U52(z0, z1), x1))) A__U61(tt, U21(U53(z0), x1)) -> c26(A__LENGTH(a__U21(a__U53(mark(z0)), x1)), MARK(U21(U53(z0), x1))) A__U61(tt, U21(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U61(mark(z0), z1), x1)), MARK(U21(U61(z0, z1), x1))) A__U61(tt, U21(length(z0), x1)) -> c26(A__LENGTH(a__U21(a__length(mark(z0)), x1)), MARK(U21(length(z0), x1))) A__U61(tt, U21(and(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__and(mark(z0), z1), x1)), MARK(U21(and(z0, z1), x1))) A__U61(tt, U21(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIListKind(z0), x1)), MARK(U21(isNatIListKind(z0), x1))) A__U61(tt, U21(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), x1)), MARK(U21(isNatKind(z0), x1))) A__U61(tt, U21(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U21(cons(mark(z0), z1), x1)), MARK(U21(cons(z0, z1), x1))) A__U61(tt, U21(tt, x1)) -> c26(A__LENGTH(a__U21(tt, x1)), MARK(U21(tt, x1))) A__U61(tt, U21(s(z0), x1)) -> c26(A__LENGTH(a__U21(s(mark(z0)), x1)), MARK(U21(s(z0), x1))) A__U61(tt, U21(x0, z1)) -> c26(MARK(U21(x0, z1))) A__U61(tt, U21(0, x1)) -> c26(A__LENGTH(a__U21(0, x1))) A__U61(tt, U21(nil, x1)) -> 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c26(A__LENGTH(a__U31(a__U11(mark(z0), z1), x1)), MARK(U31(U11(z0, z1), x1))) A__U61(tt, U31(U12(z0), x1)) -> c26(A__LENGTH(a__U31(a__U12(mark(z0)), x1)), MARK(U31(U12(z0), x1))) A__U61(tt, U31(isNatList(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatList(z0), x1)), MARK(U31(isNatList(z0), x1))) A__U61(tt, U31(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U21(mark(z0), z1), x1)), MARK(U31(U21(z0, z1), x1))) A__U61(tt, U31(U22(z0), x1)) -> c26(A__LENGTH(a__U31(a__U22(mark(z0)), x1)), MARK(U31(U22(z0), x1))) A__U61(tt, U31(isNat(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNat(z0), x1)), MARK(U31(isNat(z0), x1))) A__U61(tt, U31(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U31(mark(z0), z1), x1)), MARK(U31(U31(z0, z1), x1))) A__U61(tt, U31(U32(z0), x1)) -> c26(A__LENGTH(a__U31(a__U32(mark(z0)), x1)), MARK(U31(U32(z0), x1))) A__U61(tt, U31(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(U31(U41(z0, z1, z2), x1))) A__U61(tt, U31(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U42(mark(z0), z1), x1)), MARK(U31(U42(z0, z1), x1))) A__U61(tt, U31(U43(z0), x1)) -> c26(A__LENGTH(a__U31(a__U43(mark(z0)), x1)), MARK(U31(U43(z0), x1))) A__U61(tt, U31(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatIList(z0), x1)), MARK(U31(isNatIList(z0), x1))) A__U61(tt, U31(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U31(a__U51(mark(z0), z1, z2), x1)), MARK(U31(U51(z0, z1, z2), x1))) A__U61(tt, U31(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U52(mark(z0), z1), x1)), MARK(U31(U52(z0, z1), x1))) A__U61(tt, U31(U53(z0), x1)) -> c26(A__LENGTH(a__U31(a__U53(mark(z0)), x1)), MARK(U31(U53(z0), x1))) A__U61(tt, U31(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U61(mark(z0), z1), x1)), MARK(U31(U61(z0, z1), x1))) A__U61(tt, U31(length(z0), x1)) -> c26(A__LENGTH(a__U31(a__length(mark(z0)), x1)), MARK(U31(length(z0), x1))) A__U61(tt, U31(and(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__and(mark(z0), z1), x1)), MARK(U31(and(z0, z1), x1))) A__U61(tt, U31(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatIListKind(z0), x1)), MARK(U31(isNatIListKind(z0), x1))) A__U61(tt, U31(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatKind(z0), x1)), MARK(U31(isNatKind(z0), x1))) A__U61(tt, U31(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U31(cons(mark(z0), z1), x1)), MARK(U31(cons(z0, z1), x1))) A__U61(tt, U31(tt, x1)) -> c26(A__LENGTH(a__U31(tt, x1)), MARK(U31(tt, x1))) A__U61(tt, U31(s(z0), x1)) -> c26(A__LENGTH(a__U31(s(mark(z0)), x1)), MARK(U31(s(z0), x1))) A__U61(tt, U31(x0, z1)) -> c26(MARK(U31(x0, z1))) A__U61(tt, U31(0, x1)) -> c26(A__LENGTH(a__U31(0, x1))) A__U61(tt, U31(nil, x1)) -> c26(A__LENGTH(a__U31(nil, x1))) A__U61(tt, U32(zeros)) -> c26(A__LENGTH(a__U32(a__zeros)), MARK(U32(zeros))) A__U61(tt, U32(U11(z0, z1))) -> c26(A__LENGTH(a__U32(a__U11(mark(z0), z1))), MARK(U32(U11(z0, z1)))) A__U61(tt, U32(U12(z0))) -> c26(A__LENGTH(a__U32(a__U12(mark(z0)))), MARK(U32(U12(z0)))) A__U61(tt, U32(isNatList(z0))) -> c26(A__LENGTH(a__U32(a__isNatList(z0))), MARK(U32(isNatList(z0)))) A__U61(tt, U32(U21(z0, z1))) -> c26(A__LENGTH(a__U32(a__U21(mark(z0), z1))), MARK(U32(U21(z0, z1)))) A__U61(tt, U32(U22(z0))) -> c26(A__LENGTH(a__U32(a__U22(mark(z0)))), MARK(U32(U22(z0)))) A__U61(tt, U32(isNat(z0))) -> c26(A__LENGTH(a__U32(a__isNat(z0))), MARK(U32(isNat(z0)))) A__U61(tt, U32(U31(z0, z1))) -> c26(A__LENGTH(a__U32(a__U31(mark(z0), z1))), MARK(U32(U31(z0, z1)))) A__U61(tt, U32(U32(z0))) -> c26(A__LENGTH(a__U32(a__U32(mark(z0)))), MARK(U32(U32(z0)))) A__U61(tt, U32(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U32(a__U41(mark(z0), z1, z2))), MARK(U32(U41(z0, z1, z2)))) A__U61(tt, U32(U42(z0, z1))) -> c26(A__LENGTH(a__U32(a__U42(mark(z0), z1))), MARK(U32(U42(z0, z1)))) A__U61(tt, U32(U43(z0))) -> c26(A__LENGTH(a__U32(a__U43(mark(z0)))), MARK(U32(U43(z0)))) A__U61(tt, U32(isNatIList(z0))) -> c26(A__LENGTH(a__U32(a__isNatIList(z0))), MARK(U32(isNatIList(z0)))) A__U61(tt, U32(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U32(a__U51(mark(z0), z1, z2))), MARK(U32(U51(z0, z1, z2)))) A__U61(tt, U32(U52(z0, z1))) -> c26(A__LENGTH(a__U32(a__U52(mark(z0), z1))), MARK(U32(U52(z0, z1)))) A__U61(tt, U32(U53(z0))) -> c26(A__LENGTH(a__U32(a__U53(mark(z0)))), MARK(U32(U53(z0)))) A__U61(tt, U32(U61(z0, z1))) -> c26(A__LENGTH(a__U32(a__U61(mark(z0), z1))), MARK(U32(U61(z0, z1)))) A__U61(tt, U32(length(z0))) -> c26(A__LENGTH(a__U32(a__length(mark(z0)))), MARK(U32(length(z0)))) A__U61(tt, U32(and(z0, z1))) -> c26(A__LENGTH(a__U32(a__and(mark(z0), z1))), MARK(U32(and(z0, z1)))) A__U61(tt, U32(isNatIListKind(z0))) -> c26(A__LENGTH(a__U32(a__isNatIListKind(z0))), MARK(U32(isNatIListKind(z0)))) A__U61(tt, U32(isNatKind(z0))) -> c26(A__LENGTH(a__U32(a__isNatKind(z0))), MARK(U32(isNatKind(z0)))) A__U61(tt, U32(cons(z0, z1))) -> c26(A__LENGTH(a__U32(cons(mark(z0), z1))), MARK(U32(cons(z0, z1)))) A__U61(tt, U32(0)) -> c26(A__LENGTH(a__U32(0)), MARK(U32(0))) A__U61(tt, U32(tt)) -> c26(A__LENGTH(a__U32(tt)), MARK(U32(tt))) A__U61(tt, U32(s(z0))) -> c26(A__LENGTH(a__U32(s(mark(z0)))), MARK(U32(s(z0)))) A__U61(tt, U32(nil)) -> c26(A__LENGTH(a__U32(nil)), MARK(U32(nil))) A__U61(tt, U32(x0)) -> c26(MARK(U32(x0))) A__U61(tt, U41(zeros, x1, x2)) -> c26(A__LENGTH(a__U41(a__zeros, x1, x2)), MARK(U41(zeros, x1, x2))) A__U61(tt, U41(U11(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(U41(U11(z0, z1), x1, x2))) A__U61(tt, U41(U12(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U12(mark(z0)), x1, x2)), MARK(U41(U12(z0), x1, x2))) A__U61(tt, U41(isNatList(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatList(z0), x1, x2)), MARK(U41(isNatList(z0), x1, x2))) A__U61(tt, U41(U21(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(U41(U21(z0, z1), x1, x2))) A__U61(tt, U41(U22(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U22(mark(z0)), x1, x2)), MARK(U41(U22(z0), x1, x2))) A__U61(tt, U41(isNat(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNat(z0), x1, x2)), 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MARK(U41(U52(z0, z1), x1, x2))) A__U61(tt, U41(U53(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U53(mark(z0)), x1, x2)), MARK(U41(U53(z0), x1, x2))) A__U61(tt, U41(U61(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U61(mark(z0), z1), x1, x2)), MARK(U41(U61(z0, z1), x1, x2))) A__U61(tt, U41(length(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__length(mark(z0)), x1, x2)), MARK(U41(length(z0), x1, x2))) A__U61(tt, U41(and(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__and(mark(z0), z1), x1, x2)), MARK(U41(and(z0, z1), x1, x2))) A__U61(tt, U41(isNatIListKind(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatIListKind(z0), x1, x2)), MARK(U41(isNatIListKind(z0), x1, x2))) A__U61(tt, U41(isNatKind(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatKind(z0), x1, x2)), MARK(U41(isNatKind(z0), x1, x2))) A__U61(tt, U41(cons(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(cons(mark(z0), z1), x1, x2)), MARK(U41(cons(z0, z1), x1, x2))) A__U61(tt, U41(tt, x1, x2)) -> c26(A__LENGTH(a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2))) A__U61(tt, U41(s(z0), x1, x2)) -> c26(A__LENGTH(a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2))) A__U61(tt, U41(x0, z1, z2)) -> c26(MARK(U41(x0, z1, z2))) A__U61(tt, U41(0, x1, x2)) -> c26(A__LENGTH(a__U41(0, x1, x2))) A__U61(tt, U41(nil, x1, x2)) -> c26(A__LENGTH(a__U41(nil, x1, x2))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), 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x1)) -> c26(A__LENGTH(a__U21(a__U61(mark(z0), z1), x1)), MARK(U21(U61(z0, z1), x1))) A__U61(tt, U21(length(z0), x1)) -> c26(A__LENGTH(a__U21(a__length(mark(z0)), x1)), MARK(U21(length(z0), x1))) A__U61(tt, U21(and(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__and(mark(z0), z1), x1)), MARK(U21(and(z0, z1), x1))) A__U61(tt, U21(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIListKind(z0), x1)), MARK(U21(isNatIListKind(z0), x1))) A__U61(tt, U21(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), x1)), MARK(U21(isNatKind(z0), x1))) A__U61(tt, U21(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U21(cons(mark(z0), z1), x1)), MARK(U21(cons(z0, z1), x1))) A__U61(tt, U21(tt, x1)) -> c26(A__LENGTH(a__U21(tt, x1)), MARK(U21(tt, x1))) A__U61(tt, U21(s(z0), x1)) -> c26(A__LENGTH(a__U21(s(mark(z0)), x1)), MARK(U21(s(z0), x1))) A__U61(tt, U21(x0, z1)) -> c26(MARK(U21(x0, z1))) A__U61(tt, U21(0, x1)) -> c26(A__LENGTH(a__U21(0, x1))) A__U61(tt, U21(nil, x1)) -> c26(A__LENGTH(a__U21(nil, x1))) A__U61(tt, U22(zeros)) -> c26(A__LENGTH(a__U22(a__zeros)), MARK(U22(zeros))) A__U61(tt, U22(U11(z0, z1))) -> c26(A__LENGTH(a__U22(a__U11(mark(z0), z1))), MARK(U22(U11(z0, z1)))) A__U61(tt, U22(U12(z0))) -> c26(A__LENGTH(a__U22(a__U12(mark(z0)))), MARK(U22(U12(z0)))) A__U61(tt, U22(isNatList(z0))) -> c26(A__LENGTH(a__U22(a__isNatList(z0))), MARK(U22(isNatList(z0)))) A__U61(tt, U22(U21(z0, z1))) -> c26(A__LENGTH(a__U22(a__U21(mark(z0), z1))), MARK(U22(U21(z0, z1)))) A__U61(tt, U22(U22(z0))) -> c26(A__LENGTH(a__U22(a__U22(mark(z0)))), MARK(U22(U22(z0)))) A__U61(tt, U22(isNat(z0))) -> c26(A__LENGTH(a__U22(a__isNat(z0))), MARK(U22(isNat(z0)))) A__U61(tt, U22(U31(z0, z1))) -> c26(A__LENGTH(a__U22(a__U31(mark(z0), z1))), MARK(U22(U31(z0, z1)))) A__U61(tt, U22(U32(z0))) -> c26(A__LENGTH(a__U22(a__U32(mark(z0)))), MARK(U22(U32(z0)))) A__U61(tt, U22(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U22(a__U41(mark(z0), z1, z2))), MARK(U22(U41(z0, z1, z2)))) A__U61(tt, U22(U42(z0, z1))) -> c26(A__LENGTH(a__U22(a__U42(mark(z0), z1))), MARK(U22(U42(z0, z1)))) A__U61(tt, U22(U43(z0))) -> c26(A__LENGTH(a__U22(a__U43(mark(z0)))), MARK(U22(U43(z0)))) A__U61(tt, U22(isNatIList(z0))) -> c26(A__LENGTH(a__U22(a__isNatIList(z0))), MARK(U22(isNatIList(z0)))) A__U61(tt, U22(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U22(a__U51(mark(z0), z1, z2))), MARK(U22(U51(z0, z1, z2)))) A__U61(tt, U22(U52(z0, z1))) -> c26(A__LENGTH(a__U22(a__U52(mark(z0), z1))), MARK(U22(U52(z0, z1)))) A__U61(tt, U22(U53(z0))) -> c26(A__LENGTH(a__U22(a__U53(mark(z0)))), MARK(U22(U53(z0)))) A__U61(tt, U22(U61(z0, z1))) -> c26(A__LENGTH(a__U22(a__U61(mark(z0), z1))), MARK(U22(U61(z0, z1)))) A__U61(tt, U22(length(z0))) -> c26(A__LENGTH(a__U22(a__length(mark(z0)))), MARK(U22(length(z0)))) A__U61(tt, U22(and(z0, z1))) -> c26(A__LENGTH(a__U22(a__and(mark(z0), z1))), MARK(U22(and(z0, z1)))) A__U61(tt, U22(isNatIListKind(z0))) -> c26(A__LENGTH(a__U22(a__isNatIListKind(z0))), MARK(U22(isNatIListKind(z0)))) A__U61(tt, U22(isNatKind(z0))) -> c26(A__LENGTH(a__U22(a__isNatKind(z0))), MARK(U22(isNatKind(z0)))) A__U61(tt, U22(cons(z0, z1))) -> c26(A__LENGTH(a__U22(cons(mark(z0), z1))), MARK(U22(cons(z0, z1)))) A__U61(tt, U22(0)) -> c26(A__LENGTH(a__U22(0)), MARK(U22(0))) A__U61(tt, U22(tt)) -> c26(A__LENGTH(a__U22(tt)), MARK(U22(tt))) A__U61(tt, U22(s(z0))) -> c26(A__LENGTH(a__U22(s(mark(z0)))), MARK(U22(s(z0)))) A__U61(tt, U22(nil)) -> c26(A__LENGTH(a__U22(nil)), MARK(U22(nil))) A__U61(tt, U22(x0)) -> c26(MARK(U22(x0))) A__U61(tt, isNat(length(z0))) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), z0)), MARK(isNat(length(z0)))) A__U61(tt, isNat(s(z0))) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), z0)), MARK(isNat(s(z0)))) A__U61(tt, isNat(0)) -> c26(MARK(isNat(0))) A__U61(tt, isNat(z0)) -> c26(MARK(isNat(z0))) A__U61(tt, U31(zeros, x1)) -> c26(A__LENGTH(a__U31(a__zeros, x1)), MARK(U31(zeros, x1))) A__U61(tt, U31(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U11(mark(z0), z1), x1)), MARK(U31(U11(z0, z1), x1))) A__U61(tt, U31(U12(z0), x1)) -> c26(A__LENGTH(a__U31(a__U12(mark(z0)), x1)), MARK(U31(U12(z0), x1))) A__U61(tt, U31(isNatList(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatList(z0), x1)), MARK(U31(isNatList(z0), x1))) A__U61(tt, U31(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U21(mark(z0), z1), x1)), MARK(U31(U21(z0, z1), x1))) A__U61(tt, U31(U22(z0), x1)) -> c26(A__LENGTH(a__U31(a__U22(mark(z0)), x1)), MARK(U31(U22(z0), x1))) A__U61(tt, U31(isNat(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNat(z0), x1)), MARK(U31(isNat(z0), x1))) A__U61(tt, U31(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U31(mark(z0), z1), x1)), MARK(U31(U31(z0, z1), x1))) A__U61(tt, U31(U32(z0), x1)) -> c26(A__LENGTH(a__U31(a__U32(mark(z0)), x1)), MARK(U31(U32(z0), x1))) A__U61(tt, U31(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(U31(U41(z0, z1, z2), x1))) A__U61(tt, U31(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U42(mark(z0), z1), x1)), MARK(U31(U42(z0, z1), x1))) A__U61(tt, U31(U43(z0), x1)) -> c26(A__LENGTH(a__U31(a__U43(mark(z0)), x1)), MARK(U31(U43(z0), x1))) A__U61(tt, U31(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatIList(z0), x1)), MARK(U31(isNatIList(z0), x1))) A__U61(tt, U31(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U31(a__U51(mark(z0), z1, z2), x1)), MARK(U31(U51(z0, z1, z2), x1))) A__U61(tt, U31(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U52(mark(z0), z1), x1)), MARK(U31(U52(z0, z1), x1))) A__U61(tt, U31(U53(z0), x1)) -> c26(A__LENGTH(a__U31(a__U53(mark(z0)), x1)), MARK(U31(U53(z0), x1))) A__U61(tt, U31(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U61(mark(z0), z1), x1)), MARK(U31(U61(z0, z1), x1))) A__U61(tt, U31(length(z0), x1)) -> c26(A__LENGTH(a__U31(a__length(mark(z0)), x1)), MARK(U31(length(z0), x1))) A__U61(tt, U31(and(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__and(mark(z0), z1), x1)), MARK(U31(and(z0, z1), x1))) A__U61(tt, U31(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatIListKind(z0), x1)), MARK(U31(isNatIListKind(z0), x1))) A__U61(tt, U31(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatKind(z0), x1)), MARK(U31(isNatKind(z0), x1))) A__U61(tt, U31(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U31(cons(mark(z0), z1), x1)), MARK(U31(cons(z0, z1), x1))) A__U61(tt, U31(tt, x1)) -> c26(A__LENGTH(a__U31(tt, x1)), MARK(U31(tt, x1))) A__U61(tt, U31(s(z0), x1)) -> c26(A__LENGTH(a__U31(s(mark(z0)), x1)), MARK(U31(s(z0), x1))) A__U61(tt, U31(x0, z1)) -> c26(MARK(U31(x0, z1))) A__U61(tt, U31(0, x1)) -> c26(A__LENGTH(a__U31(0, x1))) A__U61(tt, U31(nil, x1)) -> c26(A__LENGTH(a__U31(nil, x1))) A__U61(tt, U32(zeros)) -> c26(A__LENGTH(a__U32(a__zeros)), MARK(U32(zeros))) A__U61(tt, U32(U11(z0, z1))) -> c26(A__LENGTH(a__U32(a__U11(mark(z0), z1))), MARK(U32(U11(z0, z1)))) A__U61(tt, U32(U12(z0))) -> c26(A__LENGTH(a__U32(a__U12(mark(z0)))), MARK(U32(U12(z0)))) A__U61(tt, U32(isNatList(z0))) -> c26(A__LENGTH(a__U32(a__isNatList(z0))), MARK(U32(isNatList(z0)))) A__U61(tt, U32(U21(z0, z1))) -> c26(A__LENGTH(a__U32(a__U21(mark(z0), z1))), MARK(U32(U21(z0, z1)))) A__U61(tt, U32(U22(z0))) -> c26(A__LENGTH(a__U32(a__U22(mark(z0)))), MARK(U32(U22(z0)))) A__U61(tt, U32(isNat(z0))) -> c26(A__LENGTH(a__U32(a__isNat(z0))), MARK(U32(isNat(z0)))) A__U61(tt, U32(U31(z0, z1))) -> c26(A__LENGTH(a__U32(a__U31(mark(z0), z1))), MARK(U32(U31(z0, z1)))) A__U61(tt, U32(U32(z0))) -> c26(A__LENGTH(a__U32(a__U32(mark(z0)))), MARK(U32(U32(z0)))) A__U61(tt, U32(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U32(a__U41(mark(z0), z1, z2))), MARK(U32(U41(z0, z1, z2)))) A__U61(tt, U32(U42(z0, z1))) -> c26(A__LENGTH(a__U32(a__U42(mark(z0), z1))), MARK(U32(U42(z0, z1)))) A__U61(tt, U32(U43(z0))) -> c26(A__LENGTH(a__U32(a__U43(mark(z0)))), MARK(U32(U43(z0)))) A__U61(tt, U32(isNatIList(z0))) -> c26(A__LENGTH(a__U32(a__isNatIList(z0))), MARK(U32(isNatIList(z0)))) A__U61(tt, U32(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U32(a__U51(mark(z0), z1, z2))), MARK(U32(U51(z0, z1, z2)))) A__U61(tt, U32(U52(z0, z1))) -> c26(A__LENGTH(a__U32(a__U52(mark(z0), z1))), MARK(U32(U52(z0, z1)))) A__U61(tt, U32(U53(z0))) -> c26(A__LENGTH(a__U32(a__U53(mark(z0)))), MARK(U32(U53(z0)))) A__U61(tt, U32(U61(z0, z1))) -> c26(A__LENGTH(a__U32(a__U61(mark(z0), z1))), MARK(U32(U61(z0, z1)))) A__U61(tt, U32(length(z0))) -> c26(A__LENGTH(a__U32(a__length(mark(z0)))), MARK(U32(length(z0)))) A__U61(tt, U32(and(z0, z1))) -> c26(A__LENGTH(a__U32(a__and(mark(z0), z1))), MARK(U32(and(z0, z1)))) A__U61(tt, U32(isNatIListKind(z0))) -> c26(A__LENGTH(a__U32(a__isNatIListKind(z0))), MARK(U32(isNatIListKind(z0)))) A__U61(tt, U32(isNatKind(z0))) -> c26(A__LENGTH(a__U32(a__isNatKind(z0))), MARK(U32(isNatKind(z0)))) A__U61(tt, U32(cons(z0, z1))) -> c26(A__LENGTH(a__U32(cons(mark(z0), z1))), MARK(U32(cons(z0, z1)))) A__U61(tt, U32(0)) -> c26(A__LENGTH(a__U32(0)), MARK(U32(0))) A__U61(tt, U32(tt)) -> c26(A__LENGTH(a__U32(tt)), MARK(U32(tt))) A__U61(tt, U32(s(z0))) -> c26(A__LENGTH(a__U32(s(mark(z0)))), MARK(U32(s(z0)))) A__U61(tt, U32(nil)) -> c26(A__LENGTH(a__U32(nil)), MARK(U32(nil))) A__U61(tt, U32(x0)) -> c26(MARK(U32(x0))) A__U61(tt, U41(zeros, x1, x2)) -> c26(A__LENGTH(a__U41(a__zeros, x1, x2)), MARK(U41(zeros, x1, x2))) A__U61(tt, U41(U11(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(U41(U11(z0, z1), x1, x2))) A__U61(tt, U41(U12(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U12(mark(z0)), x1, x2)), MARK(U41(U12(z0), x1, x2))) A__U61(tt, U41(isNatList(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatList(z0), x1, x2)), MARK(U41(isNatList(z0), x1, x2))) A__U61(tt, U41(U21(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(U41(U21(z0, z1), x1, x2))) A__U61(tt, U41(U22(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U22(mark(z0)), x1, x2)), MARK(U41(U22(z0), x1, x2))) A__U61(tt, U41(isNat(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNat(z0), x1, x2)), MARK(U41(isNat(z0), x1, x2))) A__U61(tt, U41(U31(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(U41(U31(z0, z1), x1, x2))) A__U61(tt, U41(U32(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U32(mark(z0)), x1, x2)), MARK(U41(U32(z0), x1, x2))) A__U61(tt, U41(U41(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2))) A__U61(tt, U41(U42(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U42(mark(z0), z1), x1, x2)), MARK(U41(U42(z0, z1), x1, x2))) A__U61(tt, U41(U43(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U43(mark(z0)), x1, x2)), MARK(U41(U43(z0), x1, x2))) A__U61(tt, U41(isNatIList(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatIList(z0), x1, x2)), MARK(U41(isNatIList(z0), x1, x2))) A__U61(tt, U41(U51(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U41(a__U51(mark(z0), z1, z2), x1, x2)), MARK(U41(U51(z0, z1, z2), x1, x2))) A__U61(tt, U41(U52(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U52(mark(z0), z1), x1, x2)), MARK(U41(U52(z0, z1), x1, x2))) A__U61(tt, U41(U53(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U53(mark(z0)), x1, x2)), MARK(U41(U53(z0), x1, x2))) A__U61(tt, U41(U61(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U61(mark(z0), z1), x1, x2)), MARK(U41(U61(z0, z1), x1, x2))) A__U61(tt, U41(length(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__length(mark(z0)), x1, x2)), MARK(U41(length(z0), x1, x2))) A__U61(tt, U41(and(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__and(mark(z0), z1), x1, x2)), MARK(U41(and(z0, z1), x1, x2))) A__U61(tt, U41(isNatIListKind(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatIListKind(z0), x1, x2)), MARK(U41(isNatIListKind(z0), x1, x2))) A__U61(tt, U41(isNatKind(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatKind(z0), x1, x2)), MARK(U41(isNatKind(z0), x1, x2))) A__U61(tt, U41(cons(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(cons(mark(z0), z1), x1, x2)), MARK(U41(cons(z0, z1), x1, x2))) A__U61(tt, U41(tt, x1, x2)) -> c26(A__LENGTH(a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2))) A__U61(tt, U41(s(z0), x1, x2)) -> c26(A__LENGTH(a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2))) A__U61(tt, U41(x0, z1, z2)) -> c26(MARK(U41(x0, z1, z2))) A__U61(tt, U41(0, x1, x2)) -> c26(A__LENGTH(a__U41(0, x1, x2))) A__U61(tt, U41(nil, x1, x2)) -> c26(A__LENGTH(a__U41(nil, x1, 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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_1, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c14_2, c20_2 ---------------------------------------- (183) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U61(tt, U42(z0, z1)) -> c26(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) by A__U61(tt, U42(x0, z1)) -> c26(A__LENGTH(U42(mark(x0), z1)), MARK(U42(x0, z1))) A__U61(tt, U42(zeros, x1)) -> c26(A__LENGTH(a__U42(a__zeros, x1)), MARK(U42(zeros, x1))) A__U61(tt, U42(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U11(mark(z0), z1), x1)), MARK(U42(U11(z0, z1), x1))) A__U61(tt, U42(U12(z0), x1)) -> c26(A__LENGTH(a__U42(a__U12(mark(z0)), x1)), MARK(U42(U12(z0), x1))) A__U61(tt, U42(isNatList(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatList(z0), x1)), MARK(U42(isNatList(z0), x1))) A__U61(tt, U42(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U21(mark(z0), z1), x1)), MARK(U42(U21(z0, z1), x1))) A__U61(tt, U42(U22(z0), x1)) -> c26(A__LENGTH(a__U42(a__U22(mark(z0)), x1)), MARK(U42(U22(z0), x1))) A__U61(tt, U42(isNat(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNat(z0), x1)), MARK(U42(isNat(z0), x1))) A__U61(tt, U42(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U31(mark(z0), z1), x1)), MARK(U42(U31(z0, z1), x1))) A__U61(tt, U42(U32(z0), x1)) -> c26(A__LENGTH(a__U42(a__U32(mark(z0)), x1)), MARK(U42(U32(z0), x1))) A__U61(tt, U42(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U42(a__U41(mark(z0), z1, z2), x1)), MARK(U42(U41(z0, z1, z2), x1))) A__U61(tt, U42(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U42(mark(z0), z1), x1)), MARK(U42(U42(z0, z1), x1))) A__U61(tt, U42(U43(z0), x1)) -> c26(A__LENGTH(a__U42(a__U43(mark(z0)), x1)), MARK(U42(U43(z0), x1))) A__U61(tt, U42(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatIList(z0), x1)), MARK(U42(isNatIList(z0), x1))) A__U61(tt, U42(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U42(a__U51(mark(z0), z1, z2), x1)), MARK(U42(U51(z0, z1, z2), x1))) A__U61(tt, U42(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U52(mark(z0), z1), x1)), MARK(U42(U52(z0, z1), x1))) A__U61(tt, U42(U53(z0), x1)) -> c26(A__LENGTH(a__U42(a__U53(mark(z0)), x1)), MARK(U42(U53(z0), x1))) A__U61(tt, U42(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U61(mark(z0), z1), x1)), MARK(U42(U61(z0, z1), x1))) A__U61(tt, U42(length(z0), x1)) -> c26(A__LENGTH(a__U42(a__length(mark(z0)), x1)), MARK(U42(length(z0), x1))) A__U61(tt, U42(and(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__and(mark(z0), z1), x1)), MARK(U42(and(z0, z1), x1))) A__U61(tt, U42(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatIListKind(z0), x1)), MARK(U42(isNatIListKind(z0), x1))) A__U61(tt, U42(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatKind(z0), x1)), MARK(U42(isNatKind(z0), x1))) A__U61(tt, U42(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U42(cons(mark(z0), z1), x1)), MARK(U42(cons(z0, z1), x1))) A__U61(tt, U42(0, x1)) -> c26(A__LENGTH(a__U42(0, x1)), MARK(U42(0, x1))) A__U61(tt, U42(tt, x1)) -> c26(A__LENGTH(a__U42(tt, x1)), MARK(U42(tt, x1))) A__U61(tt, U42(s(z0), x1)) -> c26(A__LENGTH(a__U42(s(mark(z0)), x1)), MARK(U42(s(z0), x1))) A__U61(tt, U42(nil, x1)) -> c26(A__LENGTH(a__U42(nil, x1)), MARK(U42(nil, x1))) ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> c26(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U61(tt, U12(U21(z0, z1))) -> c26(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U61(tt, U12(U22(z0))) -> c26(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U61(tt, U12(isNat(z0))) -> c26(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U61(tt, U12(U31(z0, z1))) -> c26(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U61(tt, U12(U32(z0))) -> c26(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U61(tt, U12(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U61(tt, U12(U42(z0, z1))) -> c26(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U61(tt, U12(U43(z0))) -> c26(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U61(tt, U12(isNatIList(z0))) -> c26(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U61(tt, U12(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U61(tt, U12(U52(z0, z1))) -> c26(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U61(tt, U12(U53(z0))) -> c26(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U61(tt, U12(U61(z0, z1))) -> c26(A__LENGTH(a__U12(a__U61(mark(z0), z1))), MARK(U12(U61(z0, z1)))) A__U61(tt, U12(length(z0))) -> c26(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U61(tt, U12(and(z0, 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c26(A__LENGTH(a__U32(a__isNat(z0))), MARK(U32(isNat(z0)))) A__U61(tt, U32(U31(z0, z1))) -> c26(A__LENGTH(a__U32(a__U31(mark(z0), z1))), MARK(U32(U31(z0, z1)))) A__U61(tt, U32(U32(z0))) -> c26(A__LENGTH(a__U32(a__U32(mark(z0)))), MARK(U32(U32(z0)))) A__U61(tt, U32(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U32(a__U41(mark(z0), z1, z2))), MARK(U32(U41(z0, z1, z2)))) A__U61(tt, U32(U42(z0, z1))) -> c26(A__LENGTH(a__U32(a__U42(mark(z0), z1))), MARK(U32(U42(z0, z1)))) A__U61(tt, U32(U43(z0))) -> c26(A__LENGTH(a__U32(a__U43(mark(z0)))), MARK(U32(U43(z0)))) A__U61(tt, U32(isNatIList(z0))) -> c26(A__LENGTH(a__U32(a__isNatIList(z0))), MARK(U32(isNatIList(z0)))) A__U61(tt, U32(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U32(a__U51(mark(z0), z1, z2))), MARK(U32(U51(z0, z1, z2)))) A__U61(tt, U32(U52(z0, z1))) -> c26(A__LENGTH(a__U32(a__U52(mark(z0), z1))), MARK(U32(U52(z0, z1)))) A__U61(tt, U32(U53(z0))) -> c26(A__LENGTH(a__U32(a__U53(mark(z0)))), MARK(U32(U53(z0)))) A__U61(tt, U32(U61(z0, z1))) -> c26(A__LENGTH(a__U32(a__U61(mark(z0), z1))), MARK(U32(U61(z0, z1)))) A__U61(tt, U32(length(z0))) -> c26(A__LENGTH(a__U32(a__length(mark(z0)))), MARK(U32(length(z0)))) A__U61(tt, U32(and(z0, z1))) -> c26(A__LENGTH(a__U32(a__and(mark(z0), z1))), MARK(U32(and(z0, z1)))) A__U61(tt, U32(isNatIListKind(z0))) -> c26(A__LENGTH(a__U32(a__isNatIListKind(z0))), MARK(U32(isNatIListKind(z0)))) A__U61(tt, U32(isNatKind(z0))) -> c26(A__LENGTH(a__U32(a__isNatKind(z0))), MARK(U32(isNatKind(z0)))) A__U61(tt, U32(cons(z0, z1))) -> c26(A__LENGTH(a__U32(cons(mark(z0), z1))), MARK(U32(cons(z0, z1)))) A__U61(tt, U32(0)) -> c26(A__LENGTH(a__U32(0)), MARK(U32(0))) A__U61(tt, U32(tt)) -> c26(A__LENGTH(a__U32(tt)), MARK(U32(tt))) A__U61(tt, U32(s(z0))) -> c26(A__LENGTH(a__U32(s(mark(z0)))), MARK(U32(s(z0)))) A__U61(tt, U32(nil)) -> c26(A__LENGTH(a__U32(nil)), MARK(U32(nil))) A__U61(tt, U32(x0)) -> c26(MARK(U32(x0))) A__U61(tt, U41(zeros, x1, x2)) -> c26(A__LENGTH(a__U41(a__zeros, x1, x2)), MARK(U41(zeros, x1, x2))) A__U61(tt, U41(U11(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(U41(U11(z0, z1), x1, x2))) A__U61(tt, U41(U12(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U12(mark(z0)), x1, x2)), MARK(U41(U12(z0), x1, x2))) A__U61(tt, U41(isNatList(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatList(z0), x1, x2)), MARK(U41(isNatList(z0), x1, x2))) A__U61(tt, U41(U21(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(U41(U21(z0, z1), x1, x2))) A__U61(tt, U41(U22(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U22(mark(z0)), x1, x2)), MARK(U41(U22(z0), x1, x2))) A__U61(tt, U41(isNat(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNat(z0), x1, x2)), MARK(U41(isNat(z0), x1, x2))) A__U61(tt, U41(U31(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(U41(U31(z0, z1), x1, x2))) A__U61(tt, U41(U32(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U32(mark(z0)), x1, x2)), MARK(U41(U32(z0), x1, x2))) A__U61(tt, U41(U41(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2))) A__U61(tt, U41(U42(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U42(mark(z0), z1), x1, x2)), MARK(U41(U42(z0, z1), x1, x2))) A__U61(tt, U41(U43(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U43(mark(z0)), x1, x2)), MARK(U41(U43(z0), x1, x2))) A__U61(tt, U41(isNatIList(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatIList(z0), x1, x2)), MARK(U41(isNatIList(z0), x1, x2))) A__U61(tt, U41(U51(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U41(a__U51(mark(z0), z1, z2), x1, x2)), MARK(U41(U51(z0, z1, z2), x1, x2))) A__U61(tt, U41(U52(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U52(mark(z0), z1), x1, x2)), MARK(U41(U52(z0, z1), x1, x2))) A__U61(tt, U41(U53(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U53(mark(z0)), x1, x2)), MARK(U41(U53(z0), x1, x2))) A__U61(tt, U41(U61(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U61(mark(z0), z1), x1, x2)), MARK(U41(U61(z0, z1), x1, x2))) A__U61(tt, U41(length(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__length(mark(z0)), x1, x2)), MARK(U41(length(z0), x1, x2))) A__U61(tt, U41(and(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__and(mark(z0), z1), x1, x2)), MARK(U41(and(z0, z1), x1, x2))) A__U61(tt, U41(isNatIListKind(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatIListKind(z0), x1, x2)), MARK(U41(isNatIListKind(z0), x1, x2))) A__U61(tt, U41(isNatKind(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatKind(z0), x1, x2)), MARK(U41(isNatKind(z0), x1, x2))) A__U61(tt, U41(cons(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(cons(mark(z0), z1), x1, x2)), MARK(U41(cons(z0, z1), x1, x2))) A__U61(tt, U41(tt, x1, x2)) -> c26(A__LENGTH(a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2))) A__U61(tt, U41(s(z0), x1, x2)) -> c26(A__LENGTH(a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2))) A__U61(tt, U41(x0, z1, z2)) -> c26(MARK(U41(x0, z1, z2))) A__U61(tt, U41(0, x1, x2)) -> c26(A__LENGTH(a__U41(0, x1, x2))) A__U61(tt, U41(nil, x1, x2)) -> c26(A__LENGTH(a__U41(nil, x1, x2))) A__U61(tt, U42(x0, z1)) -> c26(A__LENGTH(U42(mark(x0), z1)), MARK(U42(x0, z1))) A__U61(tt, U42(zeros, x1)) -> c26(A__LENGTH(a__U42(a__zeros, x1)), MARK(U42(zeros, x1))) A__U61(tt, U42(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U11(mark(z0), z1), x1)), MARK(U42(U11(z0, z1), x1))) A__U61(tt, U42(U12(z0), x1)) -> c26(A__LENGTH(a__U42(a__U12(mark(z0)), x1)), MARK(U42(U12(z0), x1))) A__U61(tt, U42(isNatList(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatList(z0), x1)), MARK(U42(isNatList(z0), x1))) A__U61(tt, U42(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U21(mark(z0), z1), x1)), MARK(U42(U21(z0, z1), x1))) A__U61(tt, U42(U22(z0), x1)) -> c26(A__LENGTH(a__U42(a__U22(mark(z0)), x1)), MARK(U42(U22(z0), x1))) A__U61(tt, U42(isNat(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNat(z0), x1)), MARK(U42(isNat(z0), x1))) A__U61(tt, U42(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U31(mark(z0), z1), x1)), MARK(U42(U31(z0, z1), x1))) A__U61(tt, U42(U32(z0), x1)) -> c26(A__LENGTH(a__U42(a__U32(mark(z0)), x1)), MARK(U42(U32(z0), x1))) A__U61(tt, U42(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U42(a__U41(mark(z0), z1, z2), x1)), MARK(U42(U41(z0, z1, z2), x1))) A__U61(tt, U42(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U42(mark(z0), z1), x1)), MARK(U42(U42(z0, z1), x1))) A__U61(tt, U42(U43(z0), x1)) -> c26(A__LENGTH(a__U42(a__U43(mark(z0)), x1)), MARK(U42(U43(z0), x1))) A__U61(tt, U42(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatIList(z0), x1)), MARK(U42(isNatIList(z0), x1))) A__U61(tt, U42(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U42(a__U51(mark(z0), z1, z2), x1)), MARK(U42(U51(z0, z1, z2), x1))) A__U61(tt, U42(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U52(mark(z0), z1), x1)), MARK(U42(U52(z0, z1), x1))) A__U61(tt, U42(U53(z0), x1)) -> c26(A__LENGTH(a__U42(a__U53(mark(z0)), x1)), MARK(U42(U53(z0), x1))) A__U61(tt, U42(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U61(mark(z0), z1), x1)), MARK(U42(U61(z0, z1), x1))) A__U61(tt, U42(length(z0), x1)) -> c26(A__LENGTH(a__U42(a__length(mark(z0)), x1)), MARK(U42(length(z0), x1))) A__U61(tt, U42(and(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__and(mark(z0), z1), x1)), MARK(U42(and(z0, z1), x1))) A__U61(tt, U42(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatIListKind(z0), x1)), MARK(U42(isNatIListKind(z0), x1))) A__U61(tt, U42(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatKind(z0), x1)), MARK(U42(isNatKind(z0), x1))) A__U61(tt, U42(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U42(cons(mark(z0), z1), x1)), MARK(U42(cons(z0, z1), x1))) A__U61(tt, U42(0, x1)) -> c26(A__LENGTH(a__U42(0, x1)), MARK(U42(0, x1))) A__U61(tt, U42(tt, x1)) -> c26(A__LENGTH(a__U42(tt, x1)), MARK(U42(tt, x1))) A__U61(tt, U42(s(z0), x1)) -> c26(A__LENGTH(a__U42(s(mark(z0)), x1)), MARK(U42(s(z0), x1))) A__U61(tt, U42(nil, x1)) -> c26(A__LENGTH(a__U42(nil, x1)), MARK(U42(nil, x1))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), 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A__U61(tt, U31(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U61(mark(z0), z1), x1)), MARK(U31(U61(z0, z1), x1))) A__U61(tt, U31(length(z0), x1)) -> c26(A__LENGTH(a__U31(a__length(mark(z0)), x1)), MARK(U31(length(z0), x1))) A__U61(tt, U31(and(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__and(mark(z0), z1), x1)), MARK(U31(and(z0, z1), x1))) A__U61(tt, U31(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatIListKind(z0), x1)), MARK(U31(isNatIListKind(z0), x1))) A__U61(tt, U31(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatKind(z0), x1)), MARK(U31(isNatKind(z0), x1))) A__U61(tt, U31(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U31(cons(mark(z0), z1), x1)), MARK(U31(cons(z0, z1), x1))) A__U61(tt, U31(tt, x1)) -> c26(A__LENGTH(a__U31(tt, x1)), MARK(U31(tt, x1))) A__U61(tt, U31(s(z0), x1)) -> c26(A__LENGTH(a__U31(s(mark(z0)), x1)), MARK(U31(s(z0), x1))) A__U61(tt, U31(x0, z1)) -> c26(MARK(U31(x0, z1))) A__U61(tt, U31(0, x1)) -> c26(A__LENGTH(a__U31(0, x1))) A__U61(tt, U31(nil, x1)) -> 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U32(U42(z0, z1))) -> c26(A__LENGTH(a__U32(a__U42(mark(z0), z1))), MARK(U32(U42(z0, z1)))) A__U61(tt, U32(U43(z0))) -> c26(A__LENGTH(a__U32(a__U43(mark(z0)))), MARK(U32(U43(z0)))) A__U61(tt, U32(isNatIList(z0))) -> c26(A__LENGTH(a__U32(a__isNatIList(z0))), MARK(U32(isNatIList(z0)))) A__U61(tt, U32(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U32(a__U51(mark(z0), z1, z2))), MARK(U32(U51(z0, z1, z2)))) A__U61(tt, U32(U52(z0, z1))) -> c26(A__LENGTH(a__U32(a__U52(mark(z0), z1))), MARK(U32(U52(z0, z1)))) A__U61(tt, U32(U53(z0))) -> c26(A__LENGTH(a__U32(a__U53(mark(z0)))), MARK(U32(U53(z0)))) A__U61(tt, U32(U61(z0, z1))) -> c26(A__LENGTH(a__U32(a__U61(mark(z0), z1))), MARK(U32(U61(z0, z1)))) A__U61(tt, U32(length(z0))) -> c26(A__LENGTH(a__U32(a__length(mark(z0)))), MARK(U32(length(z0)))) A__U61(tt, U32(and(z0, z1))) -> c26(A__LENGTH(a__U32(a__and(mark(z0), z1))), MARK(U32(and(z0, z1)))) A__U61(tt, U32(isNatIListKind(z0))) -> c26(A__LENGTH(a__U32(a__isNatIListKind(z0))), MARK(U32(isNatIListKind(z0)))) A__U61(tt, U32(isNatKind(z0))) -> c26(A__LENGTH(a__U32(a__isNatKind(z0))), MARK(U32(isNatKind(z0)))) A__U61(tt, U32(cons(z0, z1))) -> c26(A__LENGTH(a__U32(cons(mark(z0), z1))), MARK(U32(cons(z0, z1)))) A__U61(tt, U32(0)) -> c26(A__LENGTH(a__U32(0)), MARK(U32(0))) A__U61(tt, U32(tt)) -> c26(A__LENGTH(a__U32(tt)), MARK(U32(tt))) A__U61(tt, U32(s(z0))) -> c26(A__LENGTH(a__U32(s(mark(z0)))), MARK(U32(s(z0)))) A__U61(tt, U32(nil)) -> c26(A__LENGTH(a__U32(nil)), MARK(U32(nil))) A__U61(tt, U32(x0)) -> c26(MARK(U32(x0))) A__U61(tt, U41(zeros, x1, x2)) -> c26(A__LENGTH(a__U41(a__zeros, x1, x2)), MARK(U41(zeros, x1, x2))) A__U61(tt, U41(U11(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(U41(U11(z0, z1), x1, x2))) A__U61(tt, U41(U12(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U12(mark(z0)), x1, x2)), MARK(U41(U12(z0), x1, x2))) A__U61(tt, U41(isNatList(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatList(z0), x1, x2)), MARK(U41(isNatList(z0), x1, x2))) A__U61(tt, U41(U21(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(U41(U21(z0, z1), x1, x2))) A__U61(tt, U41(U22(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U22(mark(z0)), x1, x2)), MARK(U41(U22(z0), x1, x2))) A__U61(tt, U41(isNat(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNat(z0), x1, x2)), MARK(U41(isNat(z0), x1, x2))) A__U61(tt, U41(U31(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(U41(U31(z0, z1), x1, x2))) A__U61(tt, U41(U32(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U32(mark(z0)), x1, x2)), MARK(U41(U32(z0), x1, x2))) A__U61(tt, U41(U41(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2))) A__U61(tt, U41(U42(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U42(mark(z0), z1), x1, x2)), MARK(U41(U42(z0, z1), x1, x2))) A__U61(tt, U41(U43(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U43(mark(z0)), x1, x2)), MARK(U41(U43(z0), x1, x2))) A__U61(tt, U41(isNatIList(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatIList(z0), x1, x2)), MARK(U41(isNatIList(z0), x1, x2))) A__U61(tt, U41(U51(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U41(a__U51(mark(z0), z1, z2), x1, x2)), MARK(U41(U51(z0, z1, z2), x1, x2))) A__U61(tt, U41(U52(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U52(mark(z0), z1), x1, x2)), MARK(U41(U52(z0, z1), x1, x2))) A__U61(tt, U41(U53(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U53(mark(z0)), x1, x2)), MARK(U41(U53(z0), x1, x2))) A__U61(tt, U41(U61(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U61(mark(z0), z1), x1, x2)), MARK(U41(U61(z0, z1), x1, x2))) A__U61(tt, U41(length(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__length(mark(z0)), x1, x2)), MARK(U41(length(z0), x1, x2))) A__U61(tt, U41(and(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__and(mark(z0), z1), x1, x2)), MARK(U41(and(z0, z1), x1, x2))) A__U61(tt, U41(isNatIListKind(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatIListKind(z0), x1, x2)), MARK(U41(isNatIListKind(z0), x1, x2))) A__U61(tt, U41(isNatKind(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatKind(z0), x1, x2)), MARK(U41(isNatKind(z0), x1, x2))) A__U61(tt, U41(cons(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(cons(mark(z0), z1), x1, x2)), MARK(U41(cons(z0, z1), x1, x2))) A__U61(tt, U41(tt, x1, x2)) -> c26(A__LENGTH(a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2))) A__U61(tt, U41(s(z0), x1, x2)) -> c26(A__LENGTH(a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2))) A__U61(tt, U41(x0, z1, z2)) -> c26(MARK(U41(x0, z1, z2))) A__U61(tt, U41(0, x1, x2)) -> c26(A__LENGTH(a__U41(0, x1, x2))) A__U61(tt, U41(nil, x1, x2)) -> c26(A__LENGTH(a__U41(nil, x1, x2))) A__U61(tt, U42(x0, z1)) -> c26(A__LENGTH(U42(mark(x0), z1)), MARK(U42(x0, z1))) A__U61(tt, U42(zeros, x1)) -> c26(A__LENGTH(a__U42(a__zeros, x1)), MARK(U42(zeros, x1))) A__U61(tt, U42(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U11(mark(z0), z1), x1)), MARK(U42(U11(z0, z1), x1))) A__U61(tt, U42(U12(z0), x1)) -> c26(A__LENGTH(a__U42(a__U12(mark(z0)), x1)), MARK(U42(U12(z0), x1))) A__U61(tt, U42(isNatList(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatList(z0), x1)), MARK(U42(isNatList(z0), x1))) A__U61(tt, U42(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U21(mark(z0), z1), x1)), MARK(U42(U21(z0, z1), x1))) A__U61(tt, U42(U22(z0), x1)) -> c26(A__LENGTH(a__U42(a__U22(mark(z0)), x1)), MARK(U42(U22(z0), x1))) A__U61(tt, U42(isNat(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNat(z0), x1)), MARK(U42(isNat(z0), x1))) A__U61(tt, U42(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U31(mark(z0), z1), x1)), MARK(U42(U31(z0, z1), x1))) A__U61(tt, U42(U32(z0), x1)) -> c26(A__LENGTH(a__U42(a__U32(mark(z0)), x1)), MARK(U42(U32(z0), x1))) A__U61(tt, U42(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U42(a__U41(mark(z0), z1, z2), x1)), MARK(U42(U41(z0, z1, z2), x1))) A__U61(tt, U42(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U42(mark(z0), z1), x1)), MARK(U42(U42(z0, z1), x1))) A__U61(tt, U42(U43(z0), x1)) -> c26(A__LENGTH(a__U42(a__U43(mark(z0)), x1)), MARK(U42(U43(z0), x1))) A__U61(tt, U42(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatIList(z0), x1)), MARK(U42(isNatIList(z0), x1))) A__U61(tt, U42(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U42(a__U51(mark(z0), z1, z2), x1)), MARK(U42(U51(z0, z1, z2), x1))) A__U61(tt, U42(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U52(mark(z0), z1), x1)), MARK(U42(U52(z0, z1), x1))) A__U61(tt, U42(U53(z0), x1)) -> c26(A__LENGTH(a__U42(a__U53(mark(z0)), x1)), MARK(U42(U53(z0), x1))) A__U61(tt, U42(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U61(mark(z0), z1), x1)), MARK(U42(U61(z0, z1), x1))) A__U61(tt, U42(length(z0), x1)) -> c26(A__LENGTH(a__U42(a__length(mark(z0)), x1)), MARK(U42(length(z0), x1))) A__U61(tt, U42(and(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__and(mark(z0), z1), x1)), MARK(U42(and(z0, z1), x1))) A__U61(tt, U42(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatIListKind(z0), x1)), MARK(U42(isNatIListKind(z0), x1))) A__U61(tt, U42(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatKind(z0), x1)), MARK(U42(isNatKind(z0), x1))) A__U61(tt, U42(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U42(cons(mark(z0), z1), x1)), MARK(U42(cons(z0, z1), x1))) A__U61(tt, U42(0, x1)) -> c26(A__LENGTH(a__U42(0, x1)), MARK(U42(0, x1))) A__U61(tt, U42(tt, x1)) -> c26(A__LENGTH(a__U42(tt, x1)), MARK(U42(tt, x1))) A__U61(tt, U42(s(z0), x1)) -> c26(A__LENGTH(a__U42(s(mark(z0)), x1)), MARK(U42(s(z0), x1))) A__U61(tt, U42(nil, x1)) -> c26(A__LENGTH(a__U42(nil, x1)), MARK(U42(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_1, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c14_2, c20_2 ---------------------------------------- (185) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> c26(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U61(tt, U12(U21(z0, z1))) -> c26(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U61(tt, U12(U22(z0))) -> c26(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U61(tt, U12(isNat(z0))) -> c26(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U61(tt, U12(U31(z0, z1))) -> c26(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U61(tt, U12(U32(z0))) -> c26(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U61(tt, U12(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U61(tt, U12(U42(z0, z1))) -> c26(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U61(tt, U12(U43(z0))) -> c26(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U61(tt, U12(isNatIList(z0))) -> c26(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U61(tt, U12(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U61(tt, U12(U52(z0, z1))) -> c26(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U61(tt, U12(U53(z0))) -> c26(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U61(tt, U12(U61(z0, z1))) -> c26(A__LENGTH(a__U12(a__U61(mark(z0), z1))), MARK(U12(U61(z0, z1)))) A__U61(tt, U12(length(z0))) -> c26(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U61(tt, U12(and(z0, z1))) -> c26(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U61(tt, U12(isNatIListKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U61(tt, U12(isNatKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U61(tt, U12(cons(z0, z1))) -> c26(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U61(tt, U12(0)) -> c26(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U61(tt, U12(tt)) -> c26(A__LENGTH(a__U12(tt)), MARK(U12(tt))) A__U61(tt, U12(s(z0))) -> c26(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U61(tt, U12(nil)) -> c26(A__LENGTH(a__U12(nil)), MARK(U12(nil))) A__U61(tt, U12(x0)) -> c26(MARK(U12(x0))) A__U61(tt, isNatList(cons(z0, z1))) -> c26(A__LENGTH(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(cons(z0, z1)))) A__U61(tt, isNatList(nil)) -> c26(MARK(isNatList(nil))) A__U61(tt, isNatList(z0)) -> c26(MARK(isNatList(z0))) A__U61(tt, U21(zeros, x1)) -> c26(A__LENGTH(a__U21(a__zeros, x1)), MARK(U21(zeros, x1))) A__U61(tt, U21(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1)), MARK(U21(U11(z0, z1), x1))) A__U61(tt, U21(U12(z0), x1)) -> c26(A__LENGTH(a__U21(a__U12(mark(z0)), x1)), MARK(U21(U12(z0), x1))) A__U61(tt, U21(isNatList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatList(z0), x1)), MARK(U21(isNatList(z0), x1))) A__U61(tt, U21(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U21(mark(z0), z1), x1)), MARK(U21(U21(z0, z1), x1))) A__U61(tt, U21(U22(z0), x1)) -> c26(A__LENGTH(a__U21(a__U22(mark(z0)), x1)), MARK(U21(U22(z0), x1))) A__U61(tt, U21(isNat(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNat(z0), x1)), MARK(U21(isNat(z0), x1))) A__U61(tt, U21(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U31(mark(z0), z1), x1)), MARK(U21(U31(z0, z1), x1))) A__U61(tt, U21(U32(z0), x1)) -> c26(A__LENGTH(a__U21(a__U32(mark(z0)), x1)), MARK(U21(U32(z0), x1))) A__U61(tt, U21(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(U21(U41(z0, z1, z2), x1))) A__U61(tt, U21(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U42(mark(z0), z1), x1)), MARK(U21(U42(z0, z1), x1))) A__U61(tt, U21(U43(z0), x1)) -> c26(A__LENGTH(a__U21(a__U43(mark(z0)), x1)), MARK(U21(U43(z0), x1))) A__U61(tt, U21(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIList(z0), x1)), MARK(U21(isNatIList(z0), x1))) A__U61(tt, U21(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U51(mark(z0), z1, z2), x1)), MARK(U21(U51(z0, z1, z2), x1))) A__U61(tt, U21(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U52(mark(z0), z1), x1)), MARK(U21(U52(z0, z1), x1))) 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A__U61(tt, U41(s(z0), x1, x2)) -> c26(A__LENGTH(a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2))) A__U61(tt, U41(x0, z1, z2)) -> c26(MARK(U41(x0, z1, z2))) A__U61(tt, U41(0, x1, x2)) -> c26(A__LENGTH(a__U41(0, x1, x2))) A__U61(tt, U41(nil, x1, x2)) -> c26(A__LENGTH(a__U41(nil, x1, x2))) A__U61(tt, U42(zeros, x1)) -> c26(A__LENGTH(a__U42(a__zeros, x1)), MARK(U42(zeros, x1))) A__U61(tt, U42(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U11(mark(z0), z1), x1)), MARK(U42(U11(z0, z1), x1))) A__U61(tt, U42(U12(z0), x1)) -> c26(A__LENGTH(a__U42(a__U12(mark(z0)), x1)), MARK(U42(U12(z0), x1))) A__U61(tt, U42(isNatList(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatList(z0), x1)), MARK(U42(isNatList(z0), x1))) A__U61(tt, U42(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U21(mark(z0), z1), x1)), MARK(U42(U21(z0, z1), x1))) A__U61(tt, U42(U22(z0), x1)) -> c26(A__LENGTH(a__U42(a__U22(mark(z0)), x1)), MARK(U42(U22(z0), x1))) A__U61(tt, U42(isNat(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNat(z0), x1)), MARK(U42(isNat(z0), x1))) A__U61(tt, U42(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U31(mark(z0), z1), x1)), MARK(U42(U31(z0, z1), x1))) A__U61(tt, U42(U32(z0), x1)) -> c26(A__LENGTH(a__U42(a__U32(mark(z0)), x1)), MARK(U42(U32(z0), x1))) A__U61(tt, U42(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U42(a__U41(mark(z0), z1, z2), x1)), MARK(U42(U41(z0, z1, z2), x1))) A__U61(tt, U42(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U42(mark(z0), z1), x1)), MARK(U42(U42(z0, z1), x1))) A__U61(tt, U42(U43(z0), x1)) -> c26(A__LENGTH(a__U42(a__U43(mark(z0)), x1)), MARK(U42(U43(z0), x1))) A__U61(tt, U42(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatIList(z0), x1)), MARK(U42(isNatIList(z0), x1))) A__U61(tt, U42(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U42(a__U51(mark(z0), z1, z2), x1)), MARK(U42(U51(z0, z1, z2), x1))) A__U61(tt, U42(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U52(mark(z0), z1), x1)), MARK(U42(U52(z0, z1), x1))) A__U61(tt, U42(U53(z0), x1)) -> c26(A__LENGTH(a__U42(a__U53(mark(z0)), x1)), MARK(U42(U53(z0), x1))) A__U61(tt, U42(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U61(mark(z0), z1), x1)), MARK(U42(U61(z0, z1), x1))) A__U61(tt, U42(length(z0), x1)) -> c26(A__LENGTH(a__U42(a__length(mark(z0)), x1)), MARK(U42(length(z0), x1))) A__U61(tt, U42(and(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__and(mark(z0), z1), x1)), MARK(U42(and(z0, z1), x1))) A__U61(tt, U42(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatIListKind(z0), x1)), MARK(U42(isNatIListKind(z0), x1))) A__U61(tt, U42(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatKind(z0), x1)), MARK(U42(isNatKind(z0), x1))) A__U61(tt, U42(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U42(cons(mark(z0), z1), x1)), MARK(U42(cons(z0, z1), x1))) A__U61(tt, U42(tt, x1)) -> c26(A__LENGTH(a__U42(tt, x1)), MARK(U42(tt, x1))) A__U61(tt, U42(s(z0), x1)) -> c26(A__LENGTH(a__U42(s(mark(z0)), x1)), MARK(U42(s(z0), x1))) A__U61(tt, U42(x0, z1)) -> c26(MARK(U42(x0, z1))) A__U61(tt, U42(0, x1)) -> c26(A__LENGTH(a__U42(0, x1))) A__U61(tt, U42(nil, x1)) -> c26(A__LENGTH(a__U42(nil, x1))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> c26(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U61(tt, U12(U21(z0, z1))) -> c26(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U61(tt, U12(U22(z0))) -> c26(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U61(tt, U12(isNat(z0))) -> c26(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U61(tt, U12(U31(z0, z1))) -> c26(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U61(tt, U12(U32(z0))) -> c26(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U61(tt, U12(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U61(tt, U12(U42(z0, z1))) -> c26(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U61(tt, U12(U43(z0))) -> c26(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U61(tt, U12(isNatIList(z0))) -> c26(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U61(tt, U12(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U61(tt, U12(U52(z0, z1))) -> c26(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U61(tt, U12(U53(z0))) -> c26(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U61(tt, U12(U61(z0, z1))) -> c26(A__LENGTH(a__U12(a__U61(mark(z0), z1))), MARK(U12(U61(z0, z1)))) A__U61(tt, U12(length(z0))) -> c26(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U61(tt, U12(and(z0, z1))) -> c26(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U61(tt, U12(isNatIListKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U61(tt, U12(isNatKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U61(tt, U12(cons(z0, z1))) -> c26(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U61(tt, U12(0)) -> c26(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U61(tt, U12(tt)) -> c26(A__LENGTH(a__U12(tt)), MARK(U12(tt))) A__U61(tt, U12(s(z0))) -> c26(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U61(tt, U12(nil)) -> c26(A__LENGTH(a__U12(nil)), MARK(U12(nil))) A__U61(tt, U12(x0)) -> c26(MARK(U12(x0))) A__U61(tt, isNatList(cons(z0, z1))) -> c26(A__LENGTH(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(cons(z0, z1)))) A__U61(tt, isNatList(nil)) -> c26(MARK(isNatList(nil))) A__U61(tt, isNatList(z0)) -> c26(MARK(isNatList(z0))) A__U61(tt, U21(zeros, x1)) -> c26(A__LENGTH(a__U21(a__zeros, x1)), MARK(U21(zeros, x1))) A__U61(tt, U21(U11(z0, z1), 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c26(A__LENGTH(a__U41(a__U42(mark(z0), z1), x1, x2)), MARK(U41(U42(z0, z1), x1, x2))) A__U61(tt, U41(U43(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U43(mark(z0)), x1, x2)), MARK(U41(U43(z0), x1, x2))) A__U61(tt, U41(isNatIList(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatIList(z0), x1, x2)), MARK(U41(isNatIList(z0), x1, x2))) A__U61(tt, U41(U51(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U41(a__U51(mark(z0), z1, z2), x1, x2)), MARK(U41(U51(z0, z1, z2), x1, x2))) A__U61(tt, U41(U52(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U52(mark(z0), z1), x1, x2)), MARK(U41(U52(z0, z1), x1, x2))) A__U61(tt, U41(U53(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U53(mark(z0)), x1, x2)), MARK(U41(U53(z0), x1, x2))) A__U61(tt, U41(U61(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U61(mark(z0), z1), x1, x2)), MARK(U41(U61(z0, z1), x1, x2))) A__U61(tt, U41(length(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__length(mark(z0)), x1, x2)), MARK(U41(length(z0), x1, x2))) A__U61(tt, U41(and(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__and(mark(z0), z1), x1, x2)), MARK(U41(and(z0, z1), x1, x2))) A__U61(tt, U41(isNatIListKind(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatIListKind(z0), x1, x2)), MARK(U41(isNatIListKind(z0), x1, x2))) A__U61(tt, U41(isNatKind(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatKind(z0), x1, x2)), MARK(U41(isNatKind(z0), x1, x2))) A__U61(tt, U41(cons(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(cons(mark(z0), z1), x1, x2)), MARK(U41(cons(z0, z1), x1, x2))) A__U61(tt, U41(tt, x1, x2)) -> c26(A__LENGTH(a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2))) A__U61(tt, U41(s(z0), x1, x2)) -> c26(A__LENGTH(a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2))) A__U61(tt, U41(x0, z1, z2)) -> c26(MARK(U41(x0, z1, z2))) A__U61(tt, U41(0, x1, x2)) -> c26(A__LENGTH(a__U41(0, x1, x2))) A__U61(tt, U41(nil, x1, x2)) -> c26(A__LENGTH(a__U41(nil, x1, x2))) A__U61(tt, U42(zeros, x1)) -> c26(A__LENGTH(a__U42(a__zeros, x1)), MARK(U42(zeros, x1))) A__U61(tt, U42(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U11(mark(z0), z1), x1)), MARK(U42(U11(z0, z1), x1))) A__U61(tt, U42(U12(z0), x1)) -> c26(A__LENGTH(a__U42(a__U12(mark(z0)), x1)), MARK(U42(U12(z0), x1))) A__U61(tt, U42(isNatList(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatList(z0), x1)), MARK(U42(isNatList(z0), x1))) A__U61(tt, U42(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U21(mark(z0), z1), x1)), MARK(U42(U21(z0, z1), x1))) A__U61(tt, U42(U22(z0), x1)) -> c26(A__LENGTH(a__U42(a__U22(mark(z0)), x1)), MARK(U42(U22(z0), x1))) A__U61(tt, U42(isNat(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNat(z0), x1)), MARK(U42(isNat(z0), x1))) A__U61(tt, U42(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U31(mark(z0), z1), x1)), MARK(U42(U31(z0, z1), x1))) A__U61(tt, U42(U32(z0), x1)) -> c26(A__LENGTH(a__U42(a__U32(mark(z0)), x1)), MARK(U42(U32(z0), x1))) A__U61(tt, U42(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U42(a__U41(mark(z0), z1, z2), x1)), MARK(U42(U41(z0, z1, z2), x1))) A__U61(tt, U42(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U42(mark(z0), z1), x1)), MARK(U42(U42(z0, z1), x1))) A__U61(tt, U42(U43(z0), x1)) -> c26(A__LENGTH(a__U42(a__U43(mark(z0)), x1)), MARK(U42(U43(z0), x1))) A__U61(tt, U42(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatIList(z0), x1)), MARK(U42(isNatIList(z0), x1))) A__U61(tt, U42(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U42(a__U51(mark(z0), z1, z2), x1)), MARK(U42(U51(z0, z1, z2), x1))) A__U61(tt, U42(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U52(mark(z0), z1), x1)), MARK(U42(U52(z0, z1), x1))) A__U61(tt, U42(U53(z0), x1)) -> c26(A__LENGTH(a__U42(a__U53(mark(z0)), x1)), MARK(U42(U53(z0), x1))) A__U61(tt, U42(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U61(mark(z0), z1), x1)), MARK(U42(U61(z0, z1), x1))) A__U61(tt, U42(length(z0), x1)) -> c26(A__LENGTH(a__U42(a__length(mark(z0)), x1)), MARK(U42(length(z0), x1))) A__U61(tt, U42(and(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__and(mark(z0), z1), x1)), MARK(U42(and(z0, z1), x1))) A__U61(tt, U42(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatIListKind(z0), x1)), MARK(U42(isNatIListKind(z0), x1))) A__U61(tt, U42(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatKind(z0), x1)), MARK(U42(isNatKind(z0), x1))) A__U61(tt, U42(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U42(cons(mark(z0), z1), x1)), MARK(U42(cons(z0, z1), x1))) A__U61(tt, U42(tt, x1)) -> c26(A__LENGTH(a__U42(tt, x1)), MARK(U42(tt, x1))) A__U61(tt, U42(s(z0), x1)) -> c26(A__LENGTH(a__U42(s(mark(z0)), x1)), MARK(U42(s(z0), x1))) A__U61(tt, U42(x0, z1)) -> c26(MARK(U42(x0, z1))) A__U61(tt, U42(0, x1)) -> c26(A__LENGTH(a__U42(0, x1))) A__U61(tt, U42(nil, x1)) -> c26(A__LENGTH(a__U42(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_1, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c14_2, c20_2 ---------------------------------------- (187) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U61(tt, U43(z0)) -> c26(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) by A__U61(tt, U43(x0)) -> c26(A__LENGTH(U43(mark(x0))), MARK(U43(x0))) A__U61(tt, U43(zeros)) -> c26(A__LENGTH(a__U43(a__zeros)), MARK(U43(zeros))) A__U61(tt, U43(U11(z0, z1))) -> c26(A__LENGTH(a__U43(a__U11(mark(z0), z1))), MARK(U43(U11(z0, z1)))) A__U61(tt, U43(U12(z0))) -> c26(A__LENGTH(a__U43(a__U12(mark(z0)))), MARK(U43(U12(z0)))) A__U61(tt, U43(isNatList(z0))) -> c26(A__LENGTH(a__U43(a__isNatList(z0))), MARK(U43(isNatList(z0)))) A__U61(tt, U43(U21(z0, z1))) -> c26(A__LENGTH(a__U43(a__U21(mark(z0), z1))), MARK(U43(U21(z0, z1)))) A__U61(tt, U43(U22(z0))) -> c26(A__LENGTH(a__U43(a__U22(mark(z0)))), MARK(U43(U22(z0)))) A__U61(tt, U43(isNat(z0))) -> c26(A__LENGTH(a__U43(a__isNat(z0))), MARK(U43(isNat(z0)))) A__U61(tt, U43(U31(z0, z1))) -> c26(A__LENGTH(a__U43(a__U31(mark(z0), z1))), MARK(U43(U31(z0, z1)))) A__U61(tt, U43(U32(z0))) -> c26(A__LENGTH(a__U43(a__U32(mark(z0)))), MARK(U43(U32(z0)))) A__U61(tt, U43(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U43(a__U41(mark(z0), z1, z2))), MARK(U43(U41(z0, z1, z2)))) A__U61(tt, U43(U42(z0, z1))) -> c26(A__LENGTH(a__U43(a__U42(mark(z0), z1))), MARK(U43(U42(z0, z1)))) A__U61(tt, U43(U43(z0))) -> c26(A__LENGTH(a__U43(a__U43(mark(z0)))), MARK(U43(U43(z0)))) A__U61(tt, U43(isNatIList(z0))) -> c26(A__LENGTH(a__U43(a__isNatIList(z0))), MARK(U43(isNatIList(z0)))) A__U61(tt, U43(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U43(a__U51(mark(z0), z1, z2))), MARK(U43(U51(z0, z1, z2)))) A__U61(tt, U43(U52(z0, z1))) -> c26(A__LENGTH(a__U43(a__U52(mark(z0), z1))), MARK(U43(U52(z0, z1)))) A__U61(tt, U43(U53(z0))) -> c26(A__LENGTH(a__U43(a__U53(mark(z0)))), MARK(U43(U53(z0)))) A__U61(tt, U43(U61(z0, z1))) -> c26(A__LENGTH(a__U43(a__U61(mark(z0), z1))), MARK(U43(U61(z0, z1)))) A__U61(tt, U43(length(z0))) -> c26(A__LENGTH(a__U43(a__length(mark(z0)))), MARK(U43(length(z0)))) A__U61(tt, U43(and(z0, z1))) -> c26(A__LENGTH(a__U43(a__and(mark(z0), z1))), MARK(U43(and(z0, z1)))) A__U61(tt, U43(isNatIListKind(z0))) -> c26(A__LENGTH(a__U43(a__isNatIListKind(z0))), MARK(U43(isNatIListKind(z0)))) A__U61(tt, U43(isNatKind(z0))) -> c26(A__LENGTH(a__U43(a__isNatKind(z0))), MARK(U43(isNatKind(z0)))) A__U61(tt, U43(cons(z0, z1))) -> c26(A__LENGTH(a__U43(cons(mark(z0), z1))), MARK(U43(cons(z0, z1)))) A__U61(tt, U43(0)) -> c26(A__LENGTH(a__U43(0)), MARK(U43(0))) A__U61(tt, U43(tt)) -> c26(A__LENGTH(a__U43(tt)), MARK(U43(tt))) A__U61(tt, U43(s(z0))) -> c26(A__LENGTH(a__U43(s(mark(z0)))), MARK(U43(s(z0)))) A__U61(tt, U43(nil)) -> c26(A__LENGTH(a__U43(nil)), MARK(U43(nil))) A__U61(tt, U43(x0)) -> c26(MARK(U43(x0))) ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> c26(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U61(tt, U12(U21(z0, z1))) -> c26(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U61(tt, U12(U22(z0))) -> c26(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U61(tt, U12(isNat(z0))) -> c26(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U61(tt, U12(U31(z0, z1))) -> c26(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U61(tt, U12(U32(z0))) -> c26(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U61(tt, U12(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U61(tt, U12(U42(z0, z1))) -> c26(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U61(tt, U12(U43(z0))) -> c26(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U61(tt, U12(isNatIList(z0))) -> c26(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U61(tt, U12(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U61(tt, U12(U52(z0, z1))) -> c26(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U61(tt, U12(U53(z0))) -> c26(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U61(tt, U12(U61(z0, z1))) -> c26(A__LENGTH(a__U12(a__U61(mark(z0), z1))), MARK(U12(U61(z0, z1)))) A__U61(tt, U12(length(z0))) -> c26(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U61(tt, U12(and(z0, z1))) -> c26(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U61(tt, U12(isNatIListKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U61(tt, U12(isNatKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U61(tt, U12(cons(z0, z1))) -> c26(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U61(tt, U12(0)) -> c26(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U61(tt, U12(tt)) -> c26(A__LENGTH(a__U12(tt)), MARK(U12(tt))) A__U61(tt, U12(s(z0))) -> c26(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U61(tt, U12(nil)) -> c26(A__LENGTH(a__U12(nil)), MARK(U12(nil))) A__U61(tt, U12(x0)) -> c26(MARK(U12(x0))) A__U61(tt, isNatList(cons(z0, z1))) -> c26(A__LENGTH(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(cons(z0, z1)))) A__U61(tt, isNatList(nil)) -> c26(MARK(isNatList(nil))) A__U61(tt, isNatList(z0)) -> c26(MARK(isNatList(z0))) A__U61(tt, U21(zeros, x1)) -> c26(A__LENGTH(a__U21(a__zeros, x1)), MARK(U21(zeros, x1))) A__U61(tt, U21(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1)), MARK(U21(U11(z0, z1), x1))) A__U61(tt, U21(U12(z0), x1)) -> c26(A__LENGTH(a__U21(a__U12(mark(z0)), x1)), MARK(U21(U12(z0), x1))) A__U61(tt, U21(isNatList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatList(z0), x1)), MARK(U21(isNatList(z0), x1))) A__U61(tt, U21(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U21(mark(z0), z1), x1)), MARK(U21(U21(z0, z1), x1))) A__U61(tt, U21(U22(z0), x1)) -> c26(A__LENGTH(a__U21(a__U22(mark(z0)), x1)), MARK(U21(U22(z0), x1))) A__U61(tt, U21(isNat(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNat(z0), x1)), MARK(U21(isNat(z0), x1))) A__U61(tt, U21(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U31(mark(z0), z1), x1)), MARK(U21(U31(z0, z1), x1))) A__U61(tt, U21(U32(z0), x1)) -> c26(A__LENGTH(a__U21(a__U32(mark(z0)), x1)), MARK(U21(U32(z0), x1))) A__U61(tt, U21(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(U21(U41(z0, z1, z2), x1))) A__U61(tt, U21(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U42(mark(z0), z1), x1)), MARK(U21(U42(z0, z1), x1))) A__U61(tt, U21(U43(z0), x1)) -> c26(A__LENGTH(a__U21(a__U43(mark(z0)), x1)), MARK(U21(U43(z0), x1))) A__U61(tt, U21(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIList(z0), x1)), MARK(U21(isNatIList(z0), x1))) A__U61(tt, U21(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U51(mark(z0), z1, z2), x1)), MARK(U21(U51(z0, z1, z2), x1))) A__U61(tt, U21(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U52(mark(z0), z1), x1)), MARK(U21(U52(z0, z1), x1))) A__U61(tt, U21(U53(z0), x1)) -> c26(A__LENGTH(a__U21(a__U53(mark(z0)), x1)), MARK(U21(U53(z0), x1))) A__U61(tt, U21(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U61(mark(z0), z1), x1)), MARK(U21(U61(z0, z1), x1))) A__U61(tt, U21(length(z0), x1)) -> c26(A__LENGTH(a__U21(a__length(mark(z0)), x1)), MARK(U21(length(z0), x1))) A__U61(tt, U21(and(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__and(mark(z0), z1), x1)), MARK(U21(and(z0, z1), x1))) A__U61(tt, U21(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIListKind(z0), x1)), MARK(U21(isNatIListKind(z0), x1))) A__U61(tt, U21(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), x1)), MARK(U21(isNatKind(z0), x1))) A__U61(tt, U21(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U21(cons(mark(z0), z1), x1)), MARK(U21(cons(z0, z1), x1))) A__U61(tt, U21(tt, x1)) -> c26(A__LENGTH(a__U21(tt, x1)), MARK(U21(tt, x1))) A__U61(tt, U21(s(z0), x1)) -> c26(A__LENGTH(a__U21(s(mark(z0)), x1)), MARK(U21(s(z0), x1))) A__U61(tt, U21(x0, z1)) -> c26(MARK(U21(x0, z1))) A__U61(tt, U21(0, x1)) -> c26(A__LENGTH(a__U21(0, x1))) A__U61(tt, U21(nil, x1)) -> c26(A__LENGTH(a__U21(nil, x1))) A__U61(tt, U22(zeros)) -> c26(A__LENGTH(a__U22(a__zeros)), MARK(U22(zeros))) A__U61(tt, U22(U11(z0, z1))) -> c26(A__LENGTH(a__U22(a__U11(mark(z0), z1))), MARK(U22(U11(z0, z1)))) A__U61(tt, U22(U12(z0))) -> c26(A__LENGTH(a__U22(a__U12(mark(z0)))), MARK(U22(U12(z0)))) A__U61(tt, U22(isNatList(z0))) -> c26(A__LENGTH(a__U22(a__isNatList(z0))), MARK(U22(isNatList(z0)))) A__U61(tt, U22(U21(z0, z1))) -> c26(A__LENGTH(a__U22(a__U21(mark(z0), z1))), MARK(U22(U21(z0, z1)))) A__U61(tt, U22(U22(z0))) -> c26(A__LENGTH(a__U22(a__U22(mark(z0)))), MARK(U22(U22(z0)))) A__U61(tt, U22(isNat(z0))) -> c26(A__LENGTH(a__U22(a__isNat(z0))), MARK(U22(isNat(z0)))) A__U61(tt, U22(U31(z0, z1))) -> c26(A__LENGTH(a__U22(a__U31(mark(z0), z1))), MARK(U22(U31(z0, z1)))) A__U61(tt, U22(U32(z0))) -> c26(A__LENGTH(a__U22(a__U32(mark(z0)))), MARK(U22(U32(z0)))) A__U61(tt, U22(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U22(a__U41(mark(z0), z1, z2))), MARK(U22(U41(z0, z1, z2)))) A__U61(tt, U22(U42(z0, z1))) -> c26(A__LENGTH(a__U22(a__U42(mark(z0), z1))), MARK(U22(U42(z0, z1)))) A__U61(tt, U22(U43(z0))) -> 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U22(cons(z0, z1))) -> c26(A__LENGTH(a__U22(cons(mark(z0), z1))), MARK(U22(cons(z0, z1)))) A__U61(tt, U22(0)) -> c26(A__LENGTH(a__U22(0)), MARK(U22(0))) A__U61(tt, U22(tt)) -> c26(A__LENGTH(a__U22(tt)), MARK(U22(tt))) A__U61(tt, U22(s(z0))) -> c26(A__LENGTH(a__U22(s(mark(z0)))), MARK(U22(s(z0)))) A__U61(tt, U22(nil)) -> c26(A__LENGTH(a__U22(nil)), MARK(U22(nil))) A__U61(tt, U22(x0)) -> c26(MARK(U22(x0))) A__U61(tt, isNat(length(z0))) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), z0)), MARK(isNat(length(z0)))) A__U61(tt, isNat(s(z0))) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), z0)), MARK(isNat(s(z0)))) A__U61(tt, isNat(0)) -> c26(MARK(isNat(0))) A__U61(tt, isNat(z0)) -> c26(MARK(isNat(z0))) A__U61(tt, U31(zeros, x1)) -> c26(A__LENGTH(a__U31(a__zeros, x1)), MARK(U31(zeros, x1))) A__U61(tt, U31(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U11(mark(z0), z1), x1)), MARK(U31(U11(z0, z1), x1))) A__U61(tt, U31(U12(z0), x1)) -> c26(A__LENGTH(a__U31(a__U12(mark(z0)), x1)), MARK(U31(U12(z0), x1))) 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U42(length(z0), x1)) -> c26(A__LENGTH(a__U42(a__length(mark(z0)), x1)), MARK(U42(length(z0), x1))) A__U61(tt, U42(and(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__and(mark(z0), z1), x1)), MARK(U42(and(z0, z1), x1))) A__U61(tt, U42(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatIListKind(z0), x1)), MARK(U42(isNatIListKind(z0), x1))) A__U61(tt, U42(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatKind(z0), x1)), MARK(U42(isNatKind(z0), x1))) A__U61(tt, U42(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U42(cons(mark(z0), z1), x1)), MARK(U42(cons(z0, z1), x1))) A__U61(tt, U42(tt, x1)) -> c26(A__LENGTH(a__U42(tt, x1)), MARK(U42(tt, x1))) A__U61(tt, U42(s(z0), x1)) -> c26(A__LENGTH(a__U42(s(mark(z0)), x1)), MARK(U42(s(z0), x1))) A__U61(tt, U42(x0, z1)) -> c26(MARK(U42(x0, z1))) A__U61(tt, U42(0, x1)) -> c26(A__LENGTH(a__U42(0, x1))) A__U61(tt, U42(nil, x1)) -> c26(A__LENGTH(a__U42(nil, x1))) A__U61(tt, U43(x0)) -> c26(A__LENGTH(U43(mark(x0))), MARK(U43(x0))) A__U61(tt, U43(zeros)) -> c26(A__LENGTH(a__U43(a__zeros)), MARK(U43(zeros))) A__U61(tt, U43(U11(z0, z1))) -> c26(A__LENGTH(a__U43(a__U11(mark(z0), z1))), MARK(U43(U11(z0, z1)))) A__U61(tt, U43(U12(z0))) -> c26(A__LENGTH(a__U43(a__U12(mark(z0)))), MARK(U43(U12(z0)))) A__U61(tt, U43(isNatList(z0))) -> c26(A__LENGTH(a__U43(a__isNatList(z0))), MARK(U43(isNatList(z0)))) A__U61(tt, U43(U21(z0, z1))) -> c26(A__LENGTH(a__U43(a__U21(mark(z0), z1))), MARK(U43(U21(z0, z1)))) A__U61(tt, U43(U22(z0))) -> c26(A__LENGTH(a__U43(a__U22(mark(z0)))), MARK(U43(U22(z0)))) A__U61(tt, U43(isNat(z0))) -> c26(A__LENGTH(a__U43(a__isNat(z0))), MARK(U43(isNat(z0)))) A__U61(tt, U43(U31(z0, z1))) -> c26(A__LENGTH(a__U43(a__U31(mark(z0), z1))), MARK(U43(U31(z0, z1)))) A__U61(tt, U43(U32(z0))) -> c26(A__LENGTH(a__U43(a__U32(mark(z0)))), MARK(U43(U32(z0)))) A__U61(tt, U43(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U43(a__U41(mark(z0), z1, z2))), MARK(U43(U41(z0, z1, z2)))) A__U61(tt, U43(U42(z0, z1))) -> c26(A__LENGTH(a__U43(a__U42(mark(z0), z1))), MARK(U43(U42(z0, z1)))) A__U61(tt, U43(U43(z0))) -> c26(A__LENGTH(a__U43(a__U43(mark(z0)))), MARK(U43(U43(z0)))) A__U61(tt, U43(isNatIList(z0))) -> c26(A__LENGTH(a__U43(a__isNatIList(z0))), MARK(U43(isNatIList(z0)))) A__U61(tt, U43(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U43(a__U51(mark(z0), z1, z2))), MARK(U43(U51(z0, z1, z2)))) A__U61(tt, U43(U52(z0, z1))) -> c26(A__LENGTH(a__U43(a__U52(mark(z0), z1))), MARK(U43(U52(z0, z1)))) A__U61(tt, U43(U53(z0))) -> c26(A__LENGTH(a__U43(a__U53(mark(z0)))), MARK(U43(U53(z0)))) A__U61(tt, U43(U61(z0, z1))) -> c26(A__LENGTH(a__U43(a__U61(mark(z0), z1))), MARK(U43(U61(z0, z1)))) A__U61(tt, U43(length(z0))) -> c26(A__LENGTH(a__U43(a__length(mark(z0)))), MARK(U43(length(z0)))) A__U61(tt, U43(and(z0, z1))) -> c26(A__LENGTH(a__U43(a__and(mark(z0), z1))), MARK(U43(and(z0, z1)))) A__U61(tt, U43(isNatIListKind(z0))) -> c26(A__LENGTH(a__U43(a__isNatIListKind(z0))), MARK(U43(isNatIListKind(z0)))) A__U61(tt, U43(isNatKind(z0))) -> c26(A__LENGTH(a__U43(a__isNatKind(z0))), MARK(U43(isNatKind(z0)))) A__U61(tt, U43(cons(z0, z1))) -> c26(A__LENGTH(a__U43(cons(mark(z0), z1))), MARK(U43(cons(z0, z1)))) A__U61(tt, U43(0)) -> c26(A__LENGTH(a__U43(0)), MARK(U43(0))) A__U61(tt, U43(tt)) -> c26(A__LENGTH(a__U43(tt)), MARK(U43(tt))) A__U61(tt, U43(s(z0))) -> c26(A__LENGTH(a__U43(s(mark(z0)))), MARK(U43(s(z0)))) A__U61(tt, U43(nil)) -> c26(A__LENGTH(a__U43(nil)), MARK(U43(nil))) A__U61(tt, U43(x0)) -> c26(MARK(U43(x0))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> 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MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> 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x2)), MARK(U41(U31(z0, z1), x1, x2))) A__U61(tt, U41(U32(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U32(mark(z0)), x1, x2)), MARK(U41(U32(z0), x1, x2))) A__U61(tt, U41(U41(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2))) A__U61(tt, U41(U42(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U42(mark(z0), z1), x1, x2)), MARK(U41(U42(z0, z1), x1, x2))) A__U61(tt, U41(U43(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U43(mark(z0)), x1, x2)), MARK(U41(U43(z0), x1, x2))) A__U61(tt, U41(isNatIList(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatIList(z0), x1, x2)), MARK(U41(isNatIList(z0), x1, x2))) A__U61(tt, U41(U51(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U41(a__U51(mark(z0), z1, z2), x1, x2)), MARK(U41(U51(z0, z1, z2), x1, x2))) A__U61(tt, U41(U52(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U52(mark(z0), z1), x1, x2)), MARK(U41(U52(z0, z1), x1, x2))) A__U61(tt, U41(U53(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U53(mark(z0)), x1, x2)), MARK(U41(U53(z0), x1, x2))) A__U61(tt, U41(U61(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U61(mark(z0), z1), x1, x2)), MARK(U41(U61(z0, z1), x1, x2))) A__U61(tt, U41(length(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__length(mark(z0)), x1, x2)), MARK(U41(length(z0), x1, x2))) A__U61(tt, U41(and(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__and(mark(z0), z1), x1, x2)), MARK(U41(and(z0, z1), x1, x2))) A__U61(tt, U41(isNatIListKind(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatIListKind(z0), x1, x2)), MARK(U41(isNatIListKind(z0), x1, x2))) A__U61(tt, U41(isNatKind(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatKind(z0), x1, x2)), MARK(U41(isNatKind(z0), x1, x2))) A__U61(tt, U41(cons(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(cons(mark(z0), z1), x1, x2)), MARK(U41(cons(z0, z1), x1, x2))) A__U61(tt, U41(tt, x1, x2)) -> c26(A__LENGTH(a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2))) A__U61(tt, U41(s(z0), x1, x2)) -> c26(A__LENGTH(a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2))) A__U61(tt, U41(x0, z1, z2)) -> c26(MARK(U41(x0, z1, z2))) A__U61(tt, U41(0, x1, x2)) -> c26(A__LENGTH(a__U41(0, x1, x2))) A__U61(tt, U41(nil, x1, x2)) -> c26(A__LENGTH(a__U41(nil, x1, x2))) A__U61(tt, U42(zeros, x1)) -> c26(A__LENGTH(a__U42(a__zeros, x1)), MARK(U42(zeros, x1))) A__U61(tt, U42(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U11(mark(z0), z1), x1)), MARK(U42(U11(z0, z1), x1))) A__U61(tt, U42(U12(z0), x1)) -> c26(A__LENGTH(a__U42(a__U12(mark(z0)), x1)), MARK(U42(U12(z0), x1))) A__U61(tt, U42(isNatList(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatList(z0), x1)), MARK(U42(isNatList(z0), x1))) A__U61(tt, U42(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U21(mark(z0), z1), x1)), MARK(U42(U21(z0, z1), x1))) A__U61(tt, U42(U22(z0), x1)) -> c26(A__LENGTH(a__U42(a__U22(mark(z0)), x1)), MARK(U42(U22(z0), x1))) A__U61(tt, U42(isNat(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNat(z0), x1)), MARK(U42(isNat(z0), x1))) A__U61(tt, U42(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U31(mark(z0), z1), x1)), MARK(U42(U31(z0, z1), x1))) A__U61(tt, U42(U32(z0), x1)) -> c26(A__LENGTH(a__U42(a__U32(mark(z0)), x1)), MARK(U42(U32(z0), x1))) A__U61(tt, U42(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U42(a__U41(mark(z0), z1, z2), x1)), MARK(U42(U41(z0, z1, z2), x1))) A__U61(tt, U42(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U42(mark(z0), z1), x1)), MARK(U42(U42(z0, z1), x1))) A__U61(tt, U42(U43(z0), x1)) -> c26(A__LENGTH(a__U42(a__U43(mark(z0)), x1)), MARK(U42(U43(z0), x1))) A__U61(tt, U42(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatIList(z0), x1)), MARK(U42(isNatIList(z0), x1))) A__U61(tt, U42(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U42(a__U51(mark(z0), z1, z2), x1)), MARK(U42(U51(z0, z1, z2), x1))) A__U61(tt, U42(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U52(mark(z0), z1), x1)), MARK(U42(U52(z0, z1), x1))) A__U61(tt, U42(U53(z0), x1)) -> c26(A__LENGTH(a__U42(a__U53(mark(z0)), x1)), MARK(U42(U53(z0), x1))) A__U61(tt, U42(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U61(mark(z0), z1), x1)), MARK(U42(U61(z0, z1), x1))) A__U61(tt, U42(length(z0), x1)) -> c26(A__LENGTH(a__U42(a__length(mark(z0)), x1)), MARK(U42(length(z0), x1))) A__U61(tt, U42(and(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__and(mark(z0), z1), x1)), MARK(U42(and(z0, z1), x1))) A__U61(tt, U42(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatIListKind(z0), x1)), MARK(U42(isNatIListKind(z0), x1))) A__U61(tt, U42(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatKind(z0), x1)), MARK(U42(isNatKind(z0), x1))) A__U61(tt, U42(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U42(cons(mark(z0), z1), x1)), MARK(U42(cons(z0, z1), x1))) A__U61(tt, U42(tt, x1)) -> c26(A__LENGTH(a__U42(tt, x1)), MARK(U42(tt, x1))) A__U61(tt, U42(s(z0), x1)) -> c26(A__LENGTH(a__U42(s(mark(z0)), x1)), MARK(U42(s(z0), x1))) A__U61(tt, U42(x0, z1)) -> c26(MARK(U42(x0, z1))) A__U61(tt, U42(0, x1)) -> c26(A__LENGTH(a__U42(0, x1))) A__U61(tt, U42(nil, x1)) -> c26(A__LENGTH(a__U42(nil, x1))) A__U61(tt, U43(x0)) -> c26(A__LENGTH(U43(mark(x0))), MARK(U43(x0))) A__U61(tt, U43(zeros)) -> c26(A__LENGTH(a__U43(a__zeros)), MARK(U43(zeros))) A__U61(tt, U43(U11(z0, z1))) -> c26(A__LENGTH(a__U43(a__U11(mark(z0), z1))), MARK(U43(U11(z0, z1)))) A__U61(tt, U43(U12(z0))) -> c26(A__LENGTH(a__U43(a__U12(mark(z0)))), MARK(U43(U12(z0)))) A__U61(tt, U43(isNatList(z0))) -> c26(A__LENGTH(a__U43(a__isNatList(z0))), MARK(U43(isNatList(z0)))) A__U61(tt, U43(U21(z0, z1))) -> c26(A__LENGTH(a__U43(a__U21(mark(z0), z1))), MARK(U43(U21(z0, z1)))) A__U61(tt, U43(U22(z0))) -> c26(A__LENGTH(a__U43(a__U22(mark(z0)))), MARK(U43(U22(z0)))) A__U61(tt, U43(isNat(z0))) -> c26(A__LENGTH(a__U43(a__isNat(z0))), MARK(U43(isNat(z0)))) A__U61(tt, U43(U31(z0, z1))) -> c26(A__LENGTH(a__U43(a__U31(mark(z0), z1))), MARK(U43(U31(z0, z1)))) A__U61(tt, U43(U32(z0))) -> c26(A__LENGTH(a__U43(a__U32(mark(z0)))), MARK(U43(U32(z0)))) A__U61(tt, U43(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U43(a__U41(mark(z0), z1, z2))), MARK(U43(U41(z0, z1, z2)))) A__U61(tt, U43(U42(z0, z1))) -> c26(A__LENGTH(a__U43(a__U42(mark(z0), z1))), MARK(U43(U42(z0, z1)))) A__U61(tt, U43(U43(z0))) -> c26(A__LENGTH(a__U43(a__U43(mark(z0)))), MARK(U43(U43(z0)))) A__U61(tt, U43(isNatIList(z0))) -> c26(A__LENGTH(a__U43(a__isNatIList(z0))), MARK(U43(isNatIList(z0)))) A__U61(tt, U43(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U43(a__U51(mark(z0), z1, z2))), MARK(U43(U51(z0, z1, z2)))) A__U61(tt, U43(U52(z0, z1))) -> c26(A__LENGTH(a__U43(a__U52(mark(z0), z1))), MARK(U43(U52(z0, z1)))) A__U61(tt, U43(U53(z0))) -> c26(A__LENGTH(a__U43(a__U53(mark(z0)))), MARK(U43(U53(z0)))) A__U61(tt, U43(U61(z0, z1))) -> c26(A__LENGTH(a__U43(a__U61(mark(z0), z1))), MARK(U43(U61(z0, z1)))) A__U61(tt, U43(length(z0))) -> c26(A__LENGTH(a__U43(a__length(mark(z0)))), MARK(U43(length(z0)))) A__U61(tt, U43(and(z0, z1))) -> c26(A__LENGTH(a__U43(a__and(mark(z0), z1))), MARK(U43(and(z0, z1)))) A__U61(tt, U43(isNatIListKind(z0))) -> c26(A__LENGTH(a__U43(a__isNatIListKind(z0))), MARK(U43(isNatIListKind(z0)))) A__U61(tt, U43(isNatKind(z0))) -> c26(A__LENGTH(a__U43(a__isNatKind(z0))), MARK(U43(isNatKind(z0)))) A__U61(tt, U43(cons(z0, z1))) -> c26(A__LENGTH(a__U43(cons(mark(z0), z1))), MARK(U43(cons(z0, z1)))) A__U61(tt, U43(0)) -> c26(A__LENGTH(a__U43(0)), MARK(U43(0))) A__U61(tt, U43(tt)) -> c26(A__LENGTH(a__U43(tt)), MARK(U43(tt))) A__U61(tt, U43(s(z0))) -> c26(A__LENGTH(a__U43(s(mark(z0)))), MARK(U43(s(z0)))) A__U61(tt, U43(nil)) -> c26(A__LENGTH(a__U43(nil)), MARK(U43(nil))) A__U61(tt, U43(x0)) -> c26(MARK(U43(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_1, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c14_2, c20_2 ---------------------------------------- (189) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), 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U31(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U42(mark(z0), z1), x1)), MARK(U31(U42(z0, z1), x1))) A__U61(tt, U31(U43(z0), x1)) -> c26(A__LENGTH(a__U31(a__U43(mark(z0)), x1)), MARK(U31(U43(z0), x1))) A__U61(tt, U31(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatIList(z0), x1)), MARK(U31(isNatIList(z0), x1))) A__U61(tt, U31(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U31(a__U51(mark(z0), z1, z2), x1)), MARK(U31(U51(z0, z1, z2), x1))) A__U61(tt, U31(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U52(mark(z0), z1), x1)), MARK(U31(U52(z0, z1), x1))) A__U61(tt, U31(U53(z0), x1)) -> c26(A__LENGTH(a__U31(a__U53(mark(z0)), x1)), MARK(U31(U53(z0), x1))) A__U61(tt, U31(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U61(mark(z0), z1), x1)), MARK(U31(U61(z0, z1), x1))) A__U61(tt, U31(length(z0), x1)) -> c26(A__LENGTH(a__U31(a__length(mark(z0)), x1)), MARK(U31(length(z0), x1))) A__U61(tt, U31(and(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__and(mark(z0), z1), x1)), MARK(U31(and(z0, z1), x1))) A__U61(tt, U31(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatIListKind(z0), x1)), MARK(U31(isNatIListKind(z0), x1))) A__U61(tt, U31(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatKind(z0), x1)), MARK(U31(isNatKind(z0), x1))) A__U61(tt, U31(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U31(cons(mark(z0), z1), x1)), MARK(U31(cons(z0, z1), x1))) A__U61(tt, U31(tt, x1)) -> c26(A__LENGTH(a__U31(tt, x1)), MARK(U31(tt, x1))) A__U61(tt, U31(s(z0), x1)) -> c26(A__LENGTH(a__U31(s(mark(z0)), x1)), MARK(U31(s(z0), x1))) A__U61(tt, U31(x0, z1)) -> c26(MARK(U31(x0, z1))) A__U61(tt, U31(0, x1)) -> c26(A__LENGTH(a__U31(0, x1))) A__U61(tt, U31(nil, x1)) -> c26(A__LENGTH(a__U31(nil, x1))) A__U61(tt, U32(zeros)) -> c26(A__LENGTH(a__U32(a__zeros)), MARK(U32(zeros))) A__U61(tt, U32(U11(z0, z1))) -> c26(A__LENGTH(a__U32(a__U11(mark(z0), z1))), MARK(U32(U11(z0, z1)))) A__U61(tt, U32(U12(z0))) -> c26(A__LENGTH(a__U32(a__U12(mark(z0)))), MARK(U32(U12(z0)))) A__U61(tt, U32(isNatList(z0))) -> c26(A__LENGTH(a__U32(a__isNatList(z0))), MARK(U32(isNatList(z0)))) A__U61(tt, U32(U21(z0, z1))) -> c26(A__LENGTH(a__U32(a__U21(mark(z0), z1))), MARK(U32(U21(z0, z1)))) A__U61(tt, U32(U22(z0))) -> c26(A__LENGTH(a__U32(a__U22(mark(z0)))), MARK(U32(U22(z0)))) A__U61(tt, U32(isNat(z0))) -> c26(A__LENGTH(a__U32(a__isNat(z0))), MARK(U32(isNat(z0)))) A__U61(tt, U32(U31(z0, z1))) -> c26(A__LENGTH(a__U32(a__U31(mark(z0), z1))), MARK(U32(U31(z0, z1)))) A__U61(tt, U32(U32(z0))) -> c26(A__LENGTH(a__U32(a__U32(mark(z0)))), MARK(U32(U32(z0)))) A__U61(tt, U32(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U32(a__U41(mark(z0), z1, z2))), MARK(U32(U41(z0, z1, z2)))) A__U61(tt, U32(U42(z0, z1))) -> c26(A__LENGTH(a__U32(a__U42(mark(z0), z1))), MARK(U32(U42(z0, z1)))) A__U61(tt, U32(U43(z0))) -> c26(A__LENGTH(a__U32(a__U43(mark(z0)))), MARK(U32(U43(z0)))) A__U61(tt, U32(isNatIList(z0))) -> c26(A__LENGTH(a__U32(a__isNatIList(z0))), MARK(U32(isNatIList(z0)))) A__U61(tt, U32(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U32(a__U51(mark(z0), z1, z2))), MARK(U32(U51(z0, z1, z2)))) A__U61(tt, U32(U52(z0, z1))) -> c26(A__LENGTH(a__U32(a__U52(mark(z0), z1))), MARK(U32(U52(z0, z1)))) A__U61(tt, U32(U53(z0))) -> c26(A__LENGTH(a__U32(a__U53(mark(z0)))), MARK(U32(U53(z0)))) A__U61(tt, U32(U61(z0, z1))) -> c26(A__LENGTH(a__U32(a__U61(mark(z0), z1))), MARK(U32(U61(z0, z1)))) A__U61(tt, U32(length(z0))) -> c26(A__LENGTH(a__U32(a__length(mark(z0)))), MARK(U32(length(z0)))) A__U61(tt, U32(and(z0, z1))) -> c26(A__LENGTH(a__U32(a__and(mark(z0), z1))), MARK(U32(and(z0, z1)))) A__U61(tt, U32(isNatIListKind(z0))) -> c26(A__LENGTH(a__U32(a__isNatIListKind(z0))), MARK(U32(isNatIListKind(z0)))) A__U61(tt, U32(isNatKind(z0))) -> c26(A__LENGTH(a__U32(a__isNatKind(z0))), MARK(U32(isNatKind(z0)))) A__U61(tt, U32(cons(z0, z1))) -> c26(A__LENGTH(a__U32(cons(mark(z0), z1))), MARK(U32(cons(z0, z1)))) A__U61(tt, U32(0)) -> c26(A__LENGTH(a__U32(0)), MARK(U32(0))) A__U61(tt, U32(tt)) -> c26(A__LENGTH(a__U32(tt)), MARK(U32(tt))) A__U61(tt, U32(s(z0))) -> c26(A__LENGTH(a__U32(s(mark(z0)))), MARK(U32(s(z0)))) A__U61(tt, U32(nil)) -> c26(A__LENGTH(a__U32(nil)), MARK(U32(nil))) A__U61(tt, U32(x0)) -> c26(MARK(U32(x0))) A__U61(tt, U41(zeros, x1, x2)) -> c26(A__LENGTH(a__U41(a__zeros, x1, x2)), MARK(U41(zeros, x1, x2))) A__U61(tt, U41(U11(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(U41(U11(z0, z1), x1, x2))) A__U61(tt, U41(U12(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U12(mark(z0)), x1, x2)), MARK(U41(U12(z0), x1, x2))) A__U61(tt, U41(isNatList(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatList(z0), x1, x2)), MARK(U41(isNatList(z0), x1, x2))) A__U61(tt, U41(U21(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(U41(U21(z0, z1), x1, x2))) A__U61(tt, U41(U22(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U22(mark(z0)), x1, x2)), MARK(U41(U22(z0), x1, x2))) A__U61(tt, U41(isNat(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNat(z0), x1, x2)), MARK(U41(isNat(z0), x1, x2))) A__U61(tt, U41(U31(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(U41(U31(z0, z1), x1, x2))) A__U61(tt, U41(U32(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U32(mark(z0)), x1, x2)), MARK(U41(U32(z0), x1, x2))) A__U61(tt, U41(U41(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2))) A__U61(tt, U41(U42(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U42(mark(z0), z1), x1, x2)), MARK(U41(U42(z0, z1), x1, x2))) A__U61(tt, U41(U43(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U43(mark(z0)), x1, x2)), MARK(U41(U43(z0), x1, x2))) A__U61(tt, U41(isNatIList(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatIList(z0), x1, x2)), MARK(U41(isNatIList(z0), x1, x2))) A__U61(tt, U41(U51(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U41(a__U51(mark(z0), z1, z2), x1, x2)), MARK(U41(U51(z0, z1, z2), x1, x2))) A__U61(tt, U41(U52(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U52(mark(z0), z1), x1, x2)), MARK(U41(U52(z0, z1), x1, x2))) A__U61(tt, U41(U53(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U53(mark(z0)), x1, x2)), MARK(U41(U53(z0), x1, x2))) A__U61(tt, U41(U61(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U61(mark(z0), z1), x1, x2)), MARK(U41(U61(z0, z1), x1, x2))) A__U61(tt, U41(length(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__length(mark(z0)), x1, x2)), MARK(U41(length(z0), x1, x2))) A__U61(tt, U41(and(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__and(mark(z0), z1), x1, x2)), MARK(U41(and(z0, z1), x1, x2))) A__U61(tt, U41(isNatIListKind(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatIListKind(z0), x1, x2)), MARK(U41(isNatIListKind(z0), x1, x2))) A__U61(tt, U41(isNatKind(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatKind(z0), x1, x2)), MARK(U41(isNatKind(z0), x1, x2))) A__U61(tt, U41(cons(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(cons(mark(z0), z1), x1, x2)), MARK(U41(cons(z0, z1), x1, x2))) A__U61(tt, U41(tt, x1, x2)) -> c26(A__LENGTH(a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2))) A__U61(tt, U41(s(z0), x1, x2)) -> c26(A__LENGTH(a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2))) A__U61(tt, U41(x0, z1, z2)) -> c26(MARK(U41(x0, z1, z2))) A__U61(tt, U41(0, x1, x2)) -> c26(A__LENGTH(a__U41(0, x1, x2))) A__U61(tt, U41(nil, x1, x2)) -> c26(A__LENGTH(a__U41(nil, x1, x2))) A__U61(tt, U42(zeros, x1)) -> c26(A__LENGTH(a__U42(a__zeros, x1)), MARK(U42(zeros, x1))) A__U61(tt, U42(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U11(mark(z0), z1), x1)), MARK(U42(U11(z0, z1), x1))) A__U61(tt, U42(U12(z0), x1)) -> c26(A__LENGTH(a__U42(a__U12(mark(z0)), x1)), MARK(U42(U12(z0), x1))) A__U61(tt, U42(isNatList(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatList(z0), x1)), MARK(U42(isNatList(z0), x1))) A__U61(tt, U42(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U21(mark(z0), z1), x1)), MARK(U42(U21(z0, z1), x1))) A__U61(tt, U42(U22(z0), x1)) -> c26(A__LENGTH(a__U42(a__U22(mark(z0)), x1)), MARK(U42(U22(z0), x1))) A__U61(tt, U42(isNat(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNat(z0), x1)), MARK(U42(isNat(z0), x1))) A__U61(tt, U42(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U31(mark(z0), z1), x1)), MARK(U42(U31(z0, z1), x1))) A__U61(tt, U42(U32(z0), x1)) -> c26(A__LENGTH(a__U42(a__U32(mark(z0)), x1)), MARK(U42(U32(z0), x1))) A__U61(tt, U42(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U42(a__U41(mark(z0), z1, z2), x1)), MARK(U42(U41(z0, z1, z2), x1))) A__U61(tt, U42(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U42(mark(z0), z1), x1)), MARK(U42(U42(z0, z1), x1))) A__U61(tt, U42(U43(z0), x1)) -> c26(A__LENGTH(a__U42(a__U43(mark(z0)), x1)), MARK(U42(U43(z0), x1))) A__U61(tt, U42(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatIList(z0), x1)), MARK(U42(isNatIList(z0), x1))) A__U61(tt, U42(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U42(a__U51(mark(z0), z1, z2), x1)), MARK(U42(U51(z0, z1, z2), x1))) A__U61(tt, U42(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U52(mark(z0), z1), x1)), MARK(U42(U52(z0, z1), x1))) A__U61(tt, U42(U53(z0), x1)) -> c26(A__LENGTH(a__U42(a__U53(mark(z0)), x1)), MARK(U42(U53(z0), x1))) A__U61(tt, U42(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U61(mark(z0), z1), x1)), MARK(U42(U61(z0, z1), x1))) A__U61(tt, U42(length(z0), x1)) -> c26(A__LENGTH(a__U42(a__length(mark(z0)), x1)), MARK(U42(length(z0), x1))) A__U61(tt, U42(and(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__and(mark(z0), z1), x1)), MARK(U42(and(z0, z1), x1))) A__U61(tt, U42(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatIListKind(z0), x1)), MARK(U42(isNatIListKind(z0), x1))) A__U61(tt, U42(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatKind(z0), x1)), MARK(U42(isNatKind(z0), x1))) A__U61(tt, U42(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U42(cons(mark(z0), z1), x1)), MARK(U42(cons(z0, z1), x1))) A__U61(tt, U42(tt, x1)) -> c26(A__LENGTH(a__U42(tt, x1)), MARK(U42(tt, x1))) A__U61(tt, U42(s(z0), x1)) -> c26(A__LENGTH(a__U42(s(mark(z0)), x1)), MARK(U42(s(z0), x1))) A__U61(tt, U42(x0, z1)) -> c26(MARK(U42(x0, z1))) A__U61(tt, U42(0, x1)) -> c26(A__LENGTH(a__U42(0, x1))) A__U61(tt, U42(nil, x1)) -> c26(A__LENGTH(a__U42(nil, x1))) A__U61(tt, U43(zeros)) -> c26(A__LENGTH(a__U43(a__zeros)), MARK(U43(zeros))) A__U61(tt, U43(U11(z0, z1))) -> c26(A__LENGTH(a__U43(a__U11(mark(z0), z1))), MARK(U43(U11(z0, z1)))) A__U61(tt, U43(U12(z0))) -> c26(A__LENGTH(a__U43(a__U12(mark(z0)))), MARK(U43(U12(z0)))) A__U61(tt, U43(isNatList(z0))) -> c26(A__LENGTH(a__U43(a__isNatList(z0))), MARK(U43(isNatList(z0)))) A__U61(tt, U43(U21(z0, z1))) -> c26(A__LENGTH(a__U43(a__U21(mark(z0), z1))), MARK(U43(U21(z0, z1)))) A__U61(tt, U43(U22(z0))) -> c26(A__LENGTH(a__U43(a__U22(mark(z0)))), MARK(U43(U22(z0)))) A__U61(tt, U43(isNat(z0))) -> c26(A__LENGTH(a__U43(a__isNat(z0))), MARK(U43(isNat(z0)))) A__U61(tt, U43(U31(z0, z1))) -> c26(A__LENGTH(a__U43(a__U31(mark(z0), z1))), MARK(U43(U31(z0, z1)))) A__U61(tt, U43(U32(z0))) -> c26(A__LENGTH(a__U43(a__U32(mark(z0)))), MARK(U43(U32(z0)))) A__U61(tt, U43(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U43(a__U41(mark(z0), z1, z2))), MARK(U43(U41(z0, z1, z2)))) A__U61(tt, U43(U42(z0, z1))) -> c26(A__LENGTH(a__U43(a__U42(mark(z0), z1))), MARK(U43(U42(z0, z1)))) A__U61(tt, U43(U43(z0))) -> c26(A__LENGTH(a__U43(a__U43(mark(z0)))), MARK(U43(U43(z0)))) A__U61(tt, U43(isNatIList(z0))) -> c26(A__LENGTH(a__U43(a__isNatIList(z0))), MARK(U43(isNatIList(z0)))) A__U61(tt, U43(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U43(a__U51(mark(z0), z1, z2))), MARK(U43(U51(z0, z1, z2)))) A__U61(tt, U43(U52(z0, z1))) -> c26(A__LENGTH(a__U43(a__U52(mark(z0), z1))), MARK(U43(U52(z0, z1)))) A__U61(tt, U43(U53(z0))) -> c26(A__LENGTH(a__U43(a__U53(mark(z0)))), MARK(U43(U53(z0)))) A__U61(tt, U43(U61(z0, z1))) -> c26(A__LENGTH(a__U43(a__U61(mark(z0), z1))), MARK(U43(U61(z0, z1)))) A__U61(tt, U43(length(z0))) -> c26(A__LENGTH(a__U43(a__length(mark(z0)))), MARK(U43(length(z0)))) A__U61(tt, U43(and(z0, z1))) -> c26(A__LENGTH(a__U43(a__and(mark(z0), z1))), MARK(U43(and(z0, z1)))) A__U61(tt, U43(isNatIListKind(z0))) -> c26(A__LENGTH(a__U43(a__isNatIListKind(z0))), MARK(U43(isNatIListKind(z0)))) A__U61(tt, U43(isNatKind(z0))) -> c26(A__LENGTH(a__U43(a__isNatKind(z0))), MARK(U43(isNatKind(z0)))) A__U61(tt, U43(cons(z0, z1))) -> c26(A__LENGTH(a__U43(cons(mark(z0), z1))), MARK(U43(cons(z0, z1)))) A__U61(tt, U43(0)) -> c26(A__LENGTH(a__U43(0)), MARK(U43(0))) A__U61(tt, U43(tt)) -> c26(A__LENGTH(a__U43(tt)), MARK(U43(tt))) A__U61(tt, U43(s(z0))) -> c26(A__LENGTH(a__U43(s(mark(z0)))), MARK(U43(s(z0)))) A__U61(tt, U43(nil)) -> c26(A__LENGTH(a__U43(nil)), MARK(U43(nil))) A__U61(tt, U43(x0)) -> c26(MARK(U43(x0))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) 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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(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), 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MARK(U41(isNat(z0), x1, x2))) A__U61(tt, U41(U31(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(U41(U31(z0, z1), x1, x2))) A__U61(tt, U41(U32(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U32(mark(z0)), x1, x2)), MARK(U41(U32(z0), x1, x2))) A__U61(tt, U41(U41(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2))) A__U61(tt, U41(U42(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U42(mark(z0), z1), x1, x2)), MARK(U41(U42(z0, z1), x1, x2))) A__U61(tt, U41(U43(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U43(mark(z0)), x1, x2)), MARK(U41(U43(z0), x1, x2))) A__U61(tt, U41(isNatIList(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatIList(z0), x1, x2)), MARK(U41(isNatIList(z0), x1, x2))) A__U61(tt, U41(U51(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U41(a__U51(mark(z0), z1, z2), x1, x2)), MARK(U41(U51(z0, z1, z2), x1, x2))) A__U61(tt, U41(U52(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U52(mark(z0), z1), x1, x2)), MARK(U41(U52(z0, z1), x1, x2))) A__U61(tt, U41(U53(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U53(mark(z0)), x1, x2)), MARK(U41(U53(z0), x1, x2))) A__U61(tt, U41(U61(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U61(mark(z0), z1), x1, x2)), MARK(U41(U61(z0, z1), x1, x2))) A__U61(tt, U41(length(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__length(mark(z0)), x1, x2)), MARK(U41(length(z0), x1, x2))) A__U61(tt, U41(and(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__and(mark(z0), z1), x1, x2)), MARK(U41(and(z0, z1), x1, x2))) A__U61(tt, U41(isNatIListKind(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatIListKind(z0), x1, x2)), MARK(U41(isNatIListKind(z0), x1, x2))) A__U61(tt, U41(isNatKind(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatKind(z0), x1, x2)), MARK(U41(isNatKind(z0), x1, x2))) A__U61(tt, U41(cons(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(cons(mark(z0), z1), x1, x2)), MARK(U41(cons(z0, z1), x1, x2))) A__U61(tt, U41(tt, x1, x2)) -> c26(A__LENGTH(a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2))) A__U61(tt, U41(s(z0), x1, x2)) -> c26(A__LENGTH(a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2))) A__U61(tt, U41(x0, z1, z2)) -> c26(MARK(U41(x0, z1, z2))) A__U61(tt, U41(0, x1, x2)) -> c26(A__LENGTH(a__U41(0, x1, x2))) A__U61(tt, U41(nil, x1, x2)) -> c26(A__LENGTH(a__U41(nil, x1, x2))) A__U61(tt, U42(zeros, x1)) -> c26(A__LENGTH(a__U42(a__zeros, x1)), MARK(U42(zeros, x1))) A__U61(tt, U42(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U11(mark(z0), z1), x1)), MARK(U42(U11(z0, z1), x1))) A__U61(tt, U42(U12(z0), x1)) -> c26(A__LENGTH(a__U42(a__U12(mark(z0)), x1)), MARK(U42(U12(z0), x1))) A__U61(tt, U42(isNatList(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatList(z0), x1)), MARK(U42(isNatList(z0), x1))) A__U61(tt, U42(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U21(mark(z0), z1), x1)), MARK(U42(U21(z0, z1), x1))) A__U61(tt, U42(U22(z0), x1)) -> c26(A__LENGTH(a__U42(a__U22(mark(z0)), x1)), MARK(U42(U22(z0), x1))) A__U61(tt, U42(isNat(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNat(z0), x1)), MARK(U42(isNat(z0), x1))) A__U61(tt, U42(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U31(mark(z0), z1), x1)), MARK(U42(U31(z0, z1), x1))) A__U61(tt, U42(U32(z0), x1)) -> c26(A__LENGTH(a__U42(a__U32(mark(z0)), x1)), MARK(U42(U32(z0), x1))) A__U61(tt, U42(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U42(a__U41(mark(z0), z1, z2), x1)), MARK(U42(U41(z0, z1, z2), x1))) A__U61(tt, U42(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U42(mark(z0), z1), x1)), MARK(U42(U42(z0, z1), x1))) A__U61(tt, U42(U43(z0), x1)) -> c26(A__LENGTH(a__U42(a__U43(mark(z0)), x1)), MARK(U42(U43(z0), x1))) A__U61(tt, U42(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatIList(z0), x1)), MARK(U42(isNatIList(z0), x1))) A__U61(tt, U42(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U42(a__U51(mark(z0), z1, z2), x1)), MARK(U42(U51(z0, z1, z2), x1))) A__U61(tt, U42(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U52(mark(z0), z1), x1)), MARK(U42(U52(z0, z1), x1))) A__U61(tt, U42(U53(z0), x1)) -> c26(A__LENGTH(a__U42(a__U53(mark(z0)), x1)), MARK(U42(U53(z0), x1))) A__U61(tt, U42(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U61(mark(z0), z1), x1)), MARK(U42(U61(z0, z1), x1))) A__U61(tt, U42(length(z0), x1)) -> c26(A__LENGTH(a__U42(a__length(mark(z0)), x1)), MARK(U42(length(z0), x1))) A__U61(tt, U42(and(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__and(mark(z0), z1), x1)), MARK(U42(and(z0, z1), x1))) A__U61(tt, U42(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatIListKind(z0), x1)), MARK(U42(isNatIListKind(z0), x1))) A__U61(tt, U42(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatKind(z0), x1)), MARK(U42(isNatKind(z0), x1))) A__U61(tt, U42(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U42(cons(mark(z0), z1), x1)), MARK(U42(cons(z0, z1), x1))) A__U61(tt, U42(tt, x1)) -> c26(A__LENGTH(a__U42(tt, x1)), MARK(U42(tt, x1))) A__U61(tt, U42(s(z0), x1)) -> c26(A__LENGTH(a__U42(s(mark(z0)), x1)), MARK(U42(s(z0), x1))) A__U61(tt, U42(x0, z1)) -> c26(MARK(U42(x0, z1))) A__U61(tt, U42(0, x1)) -> c26(A__LENGTH(a__U42(0, x1))) A__U61(tt, U42(nil, x1)) -> c26(A__LENGTH(a__U42(nil, x1))) A__U61(tt, U43(zeros)) -> c26(A__LENGTH(a__U43(a__zeros)), MARK(U43(zeros))) A__U61(tt, U43(U11(z0, z1))) -> c26(A__LENGTH(a__U43(a__U11(mark(z0), z1))), MARK(U43(U11(z0, z1)))) A__U61(tt, U43(U12(z0))) -> c26(A__LENGTH(a__U43(a__U12(mark(z0)))), MARK(U43(U12(z0)))) A__U61(tt, U43(isNatList(z0))) -> c26(A__LENGTH(a__U43(a__isNatList(z0))), MARK(U43(isNatList(z0)))) A__U61(tt, U43(U21(z0, z1))) -> c26(A__LENGTH(a__U43(a__U21(mark(z0), z1))), MARK(U43(U21(z0, z1)))) A__U61(tt, U43(U22(z0))) -> c26(A__LENGTH(a__U43(a__U22(mark(z0)))), MARK(U43(U22(z0)))) A__U61(tt, U43(isNat(z0))) -> c26(A__LENGTH(a__U43(a__isNat(z0))), MARK(U43(isNat(z0)))) A__U61(tt, U43(U31(z0, z1))) -> c26(A__LENGTH(a__U43(a__U31(mark(z0), z1))), MARK(U43(U31(z0, z1)))) A__U61(tt, U43(U32(z0))) -> c26(A__LENGTH(a__U43(a__U32(mark(z0)))), MARK(U43(U32(z0)))) A__U61(tt, U43(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U43(a__U41(mark(z0), z1, z2))), MARK(U43(U41(z0, z1, z2)))) A__U61(tt, U43(U42(z0, z1))) -> c26(A__LENGTH(a__U43(a__U42(mark(z0), z1))), MARK(U43(U42(z0, z1)))) A__U61(tt, U43(U43(z0))) -> c26(A__LENGTH(a__U43(a__U43(mark(z0)))), MARK(U43(U43(z0)))) A__U61(tt, U43(isNatIList(z0))) -> c26(A__LENGTH(a__U43(a__isNatIList(z0))), MARK(U43(isNatIList(z0)))) A__U61(tt, U43(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U43(a__U51(mark(z0), z1, z2))), MARK(U43(U51(z0, z1, z2)))) A__U61(tt, U43(U52(z0, z1))) -> c26(A__LENGTH(a__U43(a__U52(mark(z0), z1))), MARK(U43(U52(z0, z1)))) A__U61(tt, U43(U53(z0))) -> c26(A__LENGTH(a__U43(a__U53(mark(z0)))), MARK(U43(U53(z0)))) A__U61(tt, U43(U61(z0, z1))) -> c26(A__LENGTH(a__U43(a__U61(mark(z0), z1))), MARK(U43(U61(z0, z1)))) A__U61(tt, U43(length(z0))) -> c26(A__LENGTH(a__U43(a__length(mark(z0)))), MARK(U43(length(z0)))) A__U61(tt, U43(and(z0, z1))) -> c26(A__LENGTH(a__U43(a__and(mark(z0), z1))), MARK(U43(and(z0, z1)))) A__U61(tt, U43(isNatIListKind(z0))) -> c26(A__LENGTH(a__U43(a__isNatIListKind(z0))), MARK(U43(isNatIListKind(z0)))) A__U61(tt, U43(isNatKind(z0))) -> c26(A__LENGTH(a__U43(a__isNatKind(z0))), MARK(U43(isNatKind(z0)))) A__U61(tt, U43(cons(z0, z1))) -> c26(A__LENGTH(a__U43(cons(mark(z0), z1))), MARK(U43(cons(z0, z1)))) A__U61(tt, U43(0)) -> c26(A__LENGTH(a__U43(0)), MARK(U43(0))) A__U61(tt, U43(tt)) -> c26(A__LENGTH(a__U43(tt)), MARK(U43(tt))) A__U61(tt, U43(s(z0))) -> c26(A__LENGTH(a__U43(s(mark(z0)))), MARK(U43(s(z0)))) A__U61(tt, U43(nil)) -> c26(A__LENGTH(a__U43(nil)), MARK(U43(nil))) A__U61(tt, U43(x0)) -> c26(MARK(U43(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_1, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c14_2, c20_2 ---------------------------------------- (191) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) by A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__U31(a__isNatIListKind(z0), z0)), MARK(isNatIList(z0))) A__U61(tt, isNatIList(zeros)) -> c26(A__LENGTH(tt), MARK(isNatIList(zeros))) A__U61(tt, isNatIList(cons(z0, z1))) -> c26(A__LENGTH(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatIList(cons(z0, z1)))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(isNatIList(z0)), MARK(isNatIList(z0))) ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> 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c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, 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c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, 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A__U61(tt, U43(U22(z0))) -> c26(A__LENGTH(a__U43(a__U22(mark(z0)))), MARK(U43(U22(z0)))) A__U61(tt, U43(isNat(z0))) -> c26(A__LENGTH(a__U43(a__isNat(z0))), MARK(U43(isNat(z0)))) A__U61(tt, U43(U31(z0, z1))) -> c26(A__LENGTH(a__U43(a__U31(mark(z0), z1))), MARK(U43(U31(z0, z1)))) A__U61(tt, U43(U32(z0))) -> c26(A__LENGTH(a__U43(a__U32(mark(z0)))), MARK(U43(U32(z0)))) A__U61(tt, U43(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U43(a__U41(mark(z0), z1, z2))), MARK(U43(U41(z0, z1, z2)))) A__U61(tt, U43(U42(z0, z1))) -> c26(A__LENGTH(a__U43(a__U42(mark(z0), z1))), MARK(U43(U42(z0, z1)))) A__U61(tt, U43(U43(z0))) -> c26(A__LENGTH(a__U43(a__U43(mark(z0)))), MARK(U43(U43(z0)))) A__U61(tt, U43(isNatIList(z0))) -> c26(A__LENGTH(a__U43(a__isNatIList(z0))), MARK(U43(isNatIList(z0)))) A__U61(tt, U43(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U43(a__U51(mark(z0), z1, z2))), MARK(U43(U51(z0, z1, z2)))) A__U61(tt, U43(U52(z0, z1))) -> c26(A__LENGTH(a__U43(a__U52(mark(z0), z1))), MARK(U43(U52(z0, z1)))) A__U61(tt, U43(U53(z0))) -> c26(A__LENGTH(a__U43(a__U53(mark(z0)))), MARK(U43(U53(z0)))) A__U61(tt, U43(U61(z0, z1))) -> c26(A__LENGTH(a__U43(a__U61(mark(z0), z1))), MARK(U43(U61(z0, z1)))) A__U61(tt, U43(length(z0))) -> c26(A__LENGTH(a__U43(a__length(mark(z0)))), MARK(U43(length(z0)))) A__U61(tt, U43(and(z0, z1))) -> c26(A__LENGTH(a__U43(a__and(mark(z0), z1))), MARK(U43(and(z0, z1)))) A__U61(tt, U43(isNatIListKind(z0))) -> c26(A__LENGTH(a__U43(a__isNatIListKind(z0))), MARK(U43(isNatIListKind(z0)))) A__U61(tt, U43(isNatKind(z0))) -> c26(A__LENGTH(a__U43(a__isNatKind(z0))), MARK(U43(isNatKind(z0)))) A__U61(tt, U43(cons(z0, z1))) -> c26(A__LENGTH(a__U43(cons(mark(z0), z1))), MARK(U43(cons(z0, z1)))) A__U61(tt, U43(0)) -> c26(A__LENGTH(a__U43(0)), MARK(U43(0))) A__U61(tt, U43(tt)) -> c26(A__LENGTH(a__U43(tt)), MARK(U43(tt))) A__U61(tt, U43(s(z0))) -> c26(A__LENGTH(a__U43(s(mark(z0)))), MARK(U43(s(z0)))) A__U61(tt, U43(nil)) -> c26(A__LENGTH(a__U43(nil)), MARK(U43(nil))) A__U61(tt, U43(x0)) -> c26(MARK(U43(x0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__U31(a__isNatIListKind(z0), z0)), MARK(isNatIList(z0))) A__U61(tt, isNatIList(zeros)) -> c26(A__LENGTH(tt), MARK(isNatIList(zeros))) A__U61(tt, isNatIList(cons(z0, z1))) -> c26(A__LENGTH(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatIList(cons(z0, z1)))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(isNatIList(z0)), MARK(isNatIList(z0))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> c26(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U61(tt, U12(U21(z0, z1))) -> c26(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U61(tt, U12(U22(z0))) -> c26(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U61(tt, U12(isNat(z0))) -> c26(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U61(tt, U12(U31(z0, z1))) -> c26(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U61(tt, U12(U32(z0))) -> c26(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U61(tt, U12(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U61(tt, U12(U42(z0, z1))) -> c26(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U61(tt, U12(U43(z0))) -> c26(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U61(tt, U12(isNatIList(z0))) -> c26(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U61(tt, U12(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U61(tt, U12(U52(z0, z1))) -> c26(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U61(tt, U12(U53(z0))) -> c26(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U61(tt, U12(U61(z0, z1))) -> c26(A__LENGTH(a__U12(a__U61(mark(z0), z1))), MARK(U12(U61(z0, z1)))) A__U61(tt, U12(length(z0))) -> c26(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U61(tt, U12(and(z0, z1))) -> c26(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U61(tt, U12(isNatIListKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U61(tt, U12(isNatKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U61(tt, U12(cons(z0, z1))) -> c26(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U61(tt, U12(0)) -> c26(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U61(tt, U12(tt)) -> c26(A__LENGTH(a__U12(tt)), MARK(U12(tt))) A__U61(tt, U12(s(z0))) -> c26(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U61(tt, U12(nil)) -> c26(A__LENGTH(a__U12(nil)), MARK(U12(nil))) A__U61(tt, U12(x0)) -> c26(MARK(U12(x0))) A__U61(tt, isNatList(cons(z0, z1))) -> c26(A__LENGTH(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(cons(z0, z1)))) A__U61(tt, isNatList(nil)) -> c26(MARK(isNatList(nil))) A__U61(tt, isNatList(z0)) -> c26(MARK(isNatList(z0))) A__U61(tt, U21(zeros, x1)) -> c26(A__LENGTH(a__U21(a__zeros, x1)), MARK(U21(zeros, x1))) A__U61(tt, U21(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1)), MARK(U21(U11(z0, z1), x1))) A__U61(tt, U21(U12(z0), x1)) -> c26(A__LENGTH(a__U21(a__U12(mark(z0)), x1)), MARK(U21(U12(z0), x1))) A__U61(tt, U21(isNatList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatList(z0), x1)), MARK(U21(isNatList(z0), x1))) A__U61(tt, U21(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U21(mark(z0), z1), x1)), MARK(U21(U21(z0, z1), x1))) A__U61(tt, U21(U22(z0), x1)) -> c26(A__LENGTH(a__U21(a__U22(mark(z0)), x1)), MARK(U21(U22(z0), x1))) A__U61(tt, U21(isNat(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNat(z0), x1)), MARK(U21(isNat(z0), x1))) A__U61(tt, U21(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U31(mark(z0), z1), x1)), MARK(U21(U31(z0, z1), x1))) A__U61(tt, U21(U32(z0), x1)) -> c26(A__LENGTH(a__U21(a__U32(mark(z0)), x1)), MARK(U21(U32(z0), x1))) A__U61(tt, U21(U41(z0, z1, z2), x1)) -> 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x2))) A__U61(tt, U41(U11(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(U41(U11(z0, z1), x1, x2))) A__U61(tt, U41(U12(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U12(mark(z0)), x1, x2)), MARK(U41(U12(z0), x1, x2))) A__U61(tt, U41(isNatList(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatList(z0), x1, x2)), MARK(U41(isNatList(z0), x1, x2))) A__U61(tt, U41(U21(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(U41(U21(z0, z1), x1, x2))) A__U61(tt, U41(U22(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U22(mark(z0)), x1, x2)), MARK(U41(U22(z0), x1, x2))) A__U61(tt, U41(isNat(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNat(z0), x1, x2)), MARK(U41(isNat(z0), x1, x2))) A__U61(tt, U41(U31(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(U41(U31(z0, z1), x1, x2))) A__U61(tt, U41(U32(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U32(mark(z0)), x1, x2)), MARK(U41(U32(z0), x1, x2))) A__U61(tt, U41(U41(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2))) A__U61(tt, U41(U42(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U42(mark(z0), z1), x1, x2)), MARK(U41(U42(z0, z1), x1, x2))) A__U61(tt, U41(U43(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U43(mark(z0)), x1, x2)), MARK(U41(U43(z0), x1, x2))) A__U61(tt, U41(isNatIList(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatIList(z0), x1, x2)), MARK(U41(isNatIList(z0), x1, x2))) A__U61(tt, U41(U51(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U41(a__U51(mark(z0), z1, z2), x1, x2)), MARK(U41(U51(z0, z1, z2), x1, x2))) A__U61(tt, U41(U52(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U52(mark(z0), z1), x1, x2)), MARK(U41(U52(z0, z1), x1, x2))) A__U61(tt, U41(U53(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U53(mark(z0)), x1, x2)), MARK(U41(U53(z0), x1, x2))) A__U61(tt, U41(U61(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U61(mark(z0), z1), x1, x2)), MARK(U41(U61(z0, z1), x1, x2))) A__U61(tt, U41(length(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__length(mark(z0)), x1, x2)), MARK(U41(length(z0), x1, x2))) A__U61(tt, U41(and(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__and(mark(z0), z1), x1, x2)), MARK(U41(and(z0, z1), x1, x2))) A__U61(tt, U41(isNatIListKind(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatIListKind(z0), x1, x2)), MARK(U41(isNatIListKind(z0), x1, x2))) A__U61(tt, U41(isNatKind(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatKind(z0), x1, x2)), MARK(U41(isNatKind(z0), x1, x2))) A__U61(tt, U41(cons(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(cons(mark(z0), z1), x1, x2)), MARK(U41(cons(z0, z1), x1, x2))) A__U61(tt, U41(tt, x1, x2)) -> c26(A__LENGTH(a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2))) A__U61(tt, U41(s(z0), x1, x2)) -> c26(A__LENGTH(a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2))) A__U61(tt, U41(x0, z1, z2)) -> c26(MARK(U41(x0, z1, z2))) A__U61(tt, U41(0, x1, x2)) -> c26(A__LENGTH(a__U41(0, x1, x2))) A__U61(tt, U41(nil, x1, x2)) -> c26(A__LENGTH(a__U41(nil, x1, x2))) A__U61(tt, U42(zeros, x1)) -> c26(A__LENGTH(a__U42(a__zeros, x1)), MARK(U42(zeros, x1))) A__U61(tt, U42(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U11(mark(z0), z1), x1)), MARK(U42(U11(z0, z1), x1))) A__U61(tt, U42(U12(z0), x1)) -> c26(A__LENGTH(a__U42(a__U12(mark(z0)), x1)), MARK(U42(U12(z0), x1))) A__U61(tt, U42(isNatList(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatList(z0), x1)), MARK(U42(isNatList(z0), x1))) A__U61(tt, U42(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U21(mark(z0), z1), x1)), MARK(U42(U21(z0, z1), x1))) A__U61(tt, U42(U22(z0), x1)) -> c26(A__LENGTH(a__U42(a__U22(mark(z0)), x1)), MARK(U42(U22(z0), x1))) A__U61(tt, U42(isNat(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNat(z0), x1)), MARK(U42(isNat(z0), x1))) A__U61(tt, U42(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U31(mark(z0), z1), x1)), MARK(U42(U31(z0, z1), x1))) A__U61(tt, U42(U32(z0), x1)) -> c26(A__LENGTH(a__U42(a__U32(mark(z0)), x1)), MARK(U42(U32(z0), x1))) A__U61(tt, U42(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U42(a__U41(mark(z0), z1, z2), x1)), MARK(U42(U41(z0, z1, z2), x1))) A__U61(tt, U42(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U42(mark(z0), z1), x1)), MARK(U42(U42(z0, z1), x1))) A__U61(tt, U42(U43(z0), x1)) -> c26(A__LENGTH(a__U42(a__U43(mark(z0)), x1)), MARK(U42(U43(z0), x1))) A__U61(tt, U42(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatIList(z0), x1)), MARK(U42(isNatIList(z0), x1))) A__U61(tt, U42(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U42(a__U51(mark(z0), z1, z2), x1)), MARK(U42(U51(z0, z1, z2), x1))) A__U61(tt, U42(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U52(mark(z0), z1), x1)), MARK(U42(U52(z0, z1), x1))) A__U61(tt, U42(U53(z0), x1)) -> c26(A__LENGTH(a__U42(a__U53(mark(z0)), x1)), MARK(U42(U53(z0), x1))) A__U61(tt, U42(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U61(mark(z0), z1), x1)), MARK(U42(U61(z0, z1), x1))) A__U61(tt, U42(length(z0), x1)) -> c26(A__LENGTH(a__U42(a__length(mark(z0)), x1)), MARK(U42(length(z0), x1))) A__U61(tt, U42(and(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__and(mark(z0), z1), x1)), MARK(U42(and(z0, z1), x1))) A__U61(tt, U42(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatIListKind(z0), x1)), MARK(U42(isNatIListKind(z0), x1))) A__U61(tt, U42(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatKind(z0), x1)), MARK(U42(isNatKind(z0), x1))) A__U61(tt, U42(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U42(cons(mark(z0), z1), x1)), MARK(U42(cons(z0, z1), x1))) A__U61(tt, U42(tt, x1)) -> c26(A__LENGTH(a__U42(tt, x1)), MARK(U42(tt, x1))) A__U61(tt, U42(s(z0), x1)) -> c26(A__LENGTH(a__U42(s(mark(z0)), x1)), MARK(U42(s(z0), x1))) A__U61(tt, U42(x0, z1)) -> c26(MARK(U42(x0, z1))) A__U61(tt, U42(0, x1)) -> c26(A__LENGTH(a__U42(0, x1))) A__U61(tt, U42(nil, x1)) -> c26(A__LENGTH(a__U42(nil, x1))) A__U61(tt, U43(zeros)) -> c26(A__LENGTH(a__U43(a__zeros)), MARK(U43(zeros))) A__U61(tt, U43(U11(z0, z1))) -> c26(A__LENGTH(a__U43(a__U11(mark(z0), z1))), MARK(U43(U11(z0, z1)))) A__U61(tt, U43(U12(z0))) -> c26(A__LENGTH(a__U43(a__U12(mark(z0)))), MARK(U43(U12(z0)))) A__U61(tt, U43(isNatList(z0))) -> c26(A__LENGTH(a__U43(a__isNatList(z0))), MARK(U43(isNatList(z0)))) A__U61(tt, U43(U21(z0, z1))) -> c26(A__LENGTH(a__U43(a__U21(mark(z0), z1))), MARK(U43(U21(z0, z1)))) A__U61(tt, U43(U22(z0))) -> c26(A__LENGTH(a__U43(a__U22(mark(z0)))), MARK(U43(U22(z0)))) A__U61(tt, U43(isNat(z0))) -> c26(A__LENGTH(a__U43(a__isNat(z0))), MARK(U43(isNat(z0)))) A__U61(tt, U43(U31(z0, z1))) -> c26(A__LENGTH(a__U43(a__U31(mark(z0), z1))), MARK(U43(U31(z0, z1)))) A__U61(tt, U43(U32(z0))) -> c26(A__LENGTH(a__U43(a__U32(mark(z0)))), MARK(U43(U32(z0)))) A__U61(tt, U43(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U43(a__U41(mark(z0), z1, z2))), MARK(U43(U41(z0, z1, z2)))) A__U61(tt, U43(U42(z0, z1))) -> c26(A__LENGTH(a__U43(a__U42(mark(z0), z1))), MARK(U43(U42(z0, z1)))) A__U61(tt, U43(U43(z0))) -> c26(A__LENGTH(a__U43(a__U43(mark(z0)))), MARK(U43(U43(z0)))) A__U61(tt, U43(isNatIList(z0))) -> c26(A__LENGTH(a__U43(a__isNatIList(z0))), MARK(U43(isNatIList(z0)))) A__U61(tt, U43(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U43(a__U51(mark(z0), z1, z2))), MARK(U43(U51(z0, z1, z2)))) A__U61(tt, U43(U52(z0, z1))) -> c26(A__LENGTH(a__U43(a__U52(mark(z0), z1))), MARK(U43(U52(z0, z1)))) A__U61(tt, U43(U53(z0))) -> c26(A__LENGTH(a__U43(a__U53(mark(z0)))), MARK(U43(U53(z0)))) A__U61(tt, U43(U61(z0, z1))) -> c26(A__LENGTH(a__U43(a__U61(mark(z0), z1))), MARK(U43(U61(z0, z1)))) A__U61(tt, U43(length(z0))) -> c26(A__LENGTH(a__U43(a__length(mark(z0)))), MARK(U43(length(z0)))) A__U61(tt, U43(and(z0, z1))) -> c26(A__LENGTH(a__U43(a__and(mark(z0), z1))), MARK(U43(and(z0, z1)))) A__U61(tt, U43(isNatIListKind(z0))) -> c26(A__LENGTH(a__U43(a__isNatIListKind(z0))), MARK(U43(isNatIListKind(z0)))) A__U61(tt, U43(isNatKind(z0))) -> c26(A__LENGTH(a__U43(a__isNatKind(z0))), MARK(U43(isNatKind(z0)))) A__U61(tt, U43(cons(z0, z1))) -> c26(A__LENGTH(a__U43(cons(mark(z0), z1))), MARK(U43(cons(z0, z1)))) A__U61(tt, U43(0)) -> c26(A__LENGTH(a__U43(0)), MARK(U43(0))) A__U61(tt, U43(tt)) -> c26(A__LENGTH(a__U43(tt)), MARK(U43(tt))) A__U61(tt, U43(s(z0))) -> c26(A__LENGTH(a__U43(s(mark(z0)))), MARK(U43(s(z0)))) A__U61(tt, U43(nil)) -> c26(A__LENGTH(a__U43(nil)), MARK(U43(nil))) A__U61(tt, U43(x0)) -> c26(MARK(U43(x0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__U31(a__isNatIListKind(z0), z0)), MARK(isNatIList(z0))) A__U61(tt, isNatIList(zeros)) -> c26(A__LENGTH(tt), MARK(isNatIList(zeros))) A__U61(tt, isNatIList(cons(z0, z1))) -> c26(A__LENGTH(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatIList(cons(z0, z1)))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(isNatIList(z0)), MARK(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_1, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c14_2, c20_2 ---------------------------------------- (193) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> c26(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U61(tt, U12(U21(z0, z1))) -> c26(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U61(tt, U12(U22(z0))) -> c26(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U61(tt, U12(isNat(z0))) -> c26(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U61(tt, U12(U31(z0, z1))) -> c26(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U61(tt, U12(U32(z0))) -> c26(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U61(tt, U12(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U61(tt, U12(U42(z0, z1))) -> c26(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U61(tt, U12(U43(z0))) -> c26(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U61(tt, U12(isNatIList(z0))) -> c26(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U61(tt, U12(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U61(tt, U12(U52(z0, z1))) -> c26(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U61(tt, U12(U53(z0))) -> c26(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U61(tt, U12(U61(z0, z1))) -> c26(A__LENGTH(a__U12(a__U61(mark(z0), z1))), MARK(U12(U61(z0, z1)))) A__U61(tt, U12(length(z0))) -> c26(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U61(tt, U12(and(z0, z1))) -> c26(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U61(tt, U12(isNatIListKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U61(tt, U12(isNatKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U61(tt, U12(cons(z0, z1))) -> c26(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U61(tt, U12(0)) -> c26(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U61(tt, U12(tt)) -> c26(A__LENGTH(a__U12(tt)), MARK(U12(tt))) A__U61(tt, U12(s(z0))) -> c26(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U61(tt, U12(nil)) -> c26(A__LENGTH(a__U12(nil)), MARK(U12(nil))) A__U61(tt, U12(x0)) -> c26(MARK(U12(x0))) A__U61(tt, isNatList(cons(z0, z1))) -> c26(A__LENGTH(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(cons(z0, z1)))) A__U61(tt, isNatList(nil)) -> c26(MARK(isNatList(nil))) A__U61(tt, isNatList(z0)) -> c26(MARK(isNatList(z0))) A__U61(tt, U21(zeros, x1)) -> c26(A__LENGTH(a__U21(a__zeros, x1)), MARK(U21(zeros, x1))) A__U61(tt, U21(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1)), MARK(U21(U11(z0, z1), x1))) A__U61(tt, U21(U12(z0), x1)) -> c26(A__LENGTH(a__U21(a__U12(mark(z0)), x1)), MARK(U21(U12(z0), x1))) A__U61(tt, U21(isNatList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatList(z0), x1)), MARK(U21(isNatList(z0), x1))) A__U61(tt, U21(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U21(mark(z0), z1), x1)), MARK(U21(U21(z0, z1), x1))) A__U61(tt, U21(U22(z0), x1)) -> c26(A__LENGTH(a__U21(a__U22(mark(z0)), x1)), MARK(U21(U22(z0), x1))) A__U61(tt, U21(isNat(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNat(z0), x1)), MARK(U21(isNat(z0), x1))) A__U61(tt, U21(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U31(mark(z0), z1), x1)), MARK(U21(U31(z0, z1), x1))) A__U61(tt, U21(U32(z0), x1)) -> c26(A__LENGTH(a__U21(a__U32(mark(z0)), x1)), MARK(U21(U32(z0), x1))) A__U61(tt, U21(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(U21(U41(z0, z1, z2), x1))) A__U61(tt, U21(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U42(mark(z0), z1), x1)), MARK(U21(U42(z0, z1), x1))) A__U61(tt, U21(U43(z0), x1)) -> c26(A__LENGTH(a__U21(a__U43(mark(z0)), x1)), MARK(U21(U43(z0), x1))) A__U61(tt, U21(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIList(z0), x1)), MARK(U21(isNatIList(z0), x1))) A__U61(tt, U21(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U51(mark(z0), z1, z2), x1)), MARK(U21(U51(z0, z1, z2), x1))) A__U61(tt, U21(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U52(mark(z0), z1), x1)), MARK(U21(U52(z0, z1), x1))) A__U61(tt, U21(U53(z0), x1)) -> c26(A__LENGTH(a__U21(a__U53(mark(z0)), x1)), MARK(U21(U53(z0), x1))) A__U61(tt, U21(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U61(mark(z0), z1), x1)), MARK(U21(U61(z0, z1), x1))) A__U61(tt, U21(length(z0), x1)) -> c26(A__LENGTH(a__U21(a__length(mark(z0)), x1)), MARK(U21(length(z0), x1))) A__U61(tt, U21(and(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__and(mark(z0), z1), x1)), MARK(U21(and(z0, z1), x1))) A__U61(tt, U21(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIListKind(z0), x1)), MARK(U21(isNatIListKind(z0), x1))) A__U61(tt, U21(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), x1)), MARK(U21(isNatKind(z0), x1))) A__U61(tt, U21(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U21(cons(mark(z0), z1), x1)), MARK(U21(cons(z0, z1), x1))) A__U61(tt, U21(tt, x1)) -> c26(A__LENGTH(a__U21(tt, x1)), MARK(U21(tt, x1))) A__U61(tt, 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A__U61(tt, U42(x0, z1)) -> c26(MARK(U42(x0, z1))) A__U61(tt, U42(0, x1)) -> c26(A__LENGTH(a__U42(0, x1))) A__U61(tt, U42(nil, x1)) -> c26(A__LENGTH(a__U42(nil, x1))) A__U61(tt, U43(zeros)) -> c26(A__LENGTH(a__U43(a__zeros)), MARK(U43(zeros))) A__U61(tt, U43(U11(z0, z1))) -> c26(A__LENGTH(a__U43(a__U11(mark(z0), z1))), MARK(U43(U11(z0, z1)))) A__U61(tt, U43(U12(z0))) -> c26(A__LENGTH(a__U43(a__U12(mark(z0)))), MARK(U43(U12(z0)))) A__U61(tt, U43(isNatList(z0))) -> c26(A__LENGTH(a__U43(a__isNatList(z0))), MARK(U43(isNatList(z0)))) A__U61(tt, U43(U21(z0, z1))) -> c26(A__LENGTH(a__U43(a__U21(mark(z0), z1))), MARK(U43(U21(z0, z1)))) A__U61(tt, U43(U22(z0))) -> c26(A__LENGTH(a__U43(a__U22(mark(z0)))), MARK(U43(U22(z0)))) A__U61(tt, U43(isNat(z0))) -> c26(A__LENGTH(a__U43(a__isNat(z0))), MARK(U43(isNat(z0)))) A__U61(tt, U43(U31(z0, z1))) -> c26(A__LENGTH(a__U43(a__U31(mark(z0), z1))), MARK(U43(U31(z0, z1)))) A__U61(tt, U43(U32(z0))) -> c26(A__LENGTH(a__U43(a__U32(mark(z0)))), MARK(U43(U32(z0)))) A__U61(tt, U43(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U43(a__U41(mark(z0), z1, z2))), MARK(U43(U41(z0, z1, z2)))) A__U61(tt, U43(U42(z0, z1))) -> c26(A__LENGTH(a__U43(a__U42(mark(z0), z1))), MARK(U43(U42(z0, z1)))) A__U61(tt, U43(U43(z0))) -> c26(A__LENGTH(a__U43(a__U43(mark(z0)))), MARK(U43(U43(z0)))) A__U61(tt, U43(isNatIList(z0))) -> c26(A__LENGTH(a__U43(a__isNatIList(z0))), MARK(U43(isNatIList(z0)))) A__U61(tt, U43(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U43(a__U51(mark(z0), z1, z2))), MARK(U43(U51(z0, z1, z2)))) A__U61(tt, U43(U52(z0, z1))) -> c26(A__LENGTH(a__U43(a__U52(mark(z0), z1))), MARK(U43(U52(z0, z1)))) A__U61(tt, U43(U53(z0))) -> c26(A__LENGTH(a__U43(a__U53(mark(z0)))), MARK(U43(U53(z0)))) A__U61(tt, U43(U61(z0, z1))) -> c26(A__LENGTH(a__U43(a__U61(mark(z0), z1))), MARK(U43(U61(z0, z1)))) A__U61(tt, U43(length(z0))) -> c26(A__LENGTH(a__U43(a__length(mark(z0)))), MARK(U43(length(z0)))) A__U61(tt, U43(and(z0, z1))) -> c26(A__LENGTH(a__U43(a__and(mark(z0), z1))), MARK(U43(and(z0, z1)))) A__U61(tt, U43(isNatIListKind(z0))) -> c26(A__LENGTH(a__U43(a__isNatIListKind(z0))), MARK(U43(isNatIListKind(z0)))) A__U61(tt, U43(isNatKind(z0))) -> c26(A__LENGTH(a__U43(a__isNatKind(z0))), MARK(U43(isNatKind(z0)))) A__U61(tt, U43(cons(z0, z1))) -> c26(A__LENGTH(a__U43(cons(mark(z0), z1))), MARK(U43(cons(z0, z1)))) A__U61(tt, U43(0)) -> c26(A__LENGTH(a__U43(0)), MARK(U43(0))) A__U61(tt, U43(tt)) -> c26(A__LENGTH(a__U43(tt)), MARK(U43(tt))) A__U61(tt, U43(s(z0))) -> c26(A__LENGTH(a__U43(s(mark(z0)))), MARK(U43(s(z0)))) A__U61(tt, U43(nil)) -> c26(A__LENGTH(a__U43(nil)), MARK(U43(nil))) A__U61(tt, U43(x0)) -> c26(MARK(U43(x0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__U31(a__isNatIListKind(z0), z0)), MARK(isNatIList(z0))) A__U61(tt, isNatIList(cons(z0, z1))) -> c26(A__LENGTH(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatIList(cons(z0, z1)))) A__U61(tt, isNatIList(zeros)) -> c26(MARK(isNatIList(zeros))) A__U61(tt, isNatIList(z0)) -> c26(MARK(isNatIList(z0))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> 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MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, 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MARK(U31(isNat(z0), x1))) A__U61(tt, U31(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U31(mark(z0), z1), x1)), MARK(U31(U31(z0, z1), x1))) A__U61(tt, U31(U32(z0), x1)) -> c26(A__LENGTH(a__U31(a__U32(mark(z0)), x1)), MARK(U31(U32(z0), x1))) A__U61(tt, U31(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(U31(U41(z0, z1, z2), x1))) A__U61(tt, U31(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U42(mark(z0), z1), x1)), MARK(U31(U42(z0, z1), x1))) A__U61(tt, U31(U43(z0), x1)) -> c26(A__LENGTH(a__U31(a__U43(mark(z0)), x1)), MARK(U31(U43(z0), x1))) A__U61(tt, U31(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatIList(z0), x1)), MARK(U31(isNatIList(z0), x1))) A__U61(tt, U31(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U31(a__U51(mark(z0), z1, z2), x1)), MARK(U31(U51(z0, z1, z2), x1))) A__U61(tt, U31(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U52(mark(z0), z1), x1)), MARK(U31(U52(z0, z1), x1))) A__U61(tt, U31(U53(z0), x1)) -> 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x2)) -> c26(A__LENGTH(a__U41(a__isNatList(z0), x1, x2)), MARK(U41(isNatList(z0), x1, x2))) A__U61(tt, U41(U21(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(U41(U21(z0, z1), x1, x2))) A__U61(tt, U41(U22(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U22(mark(z0)), x1, x2)), MARK(U41(U22(z0), x1, x2))) A__U61(tt, U41(isNat(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNat(z0), x1, x2)), MARK(U41(isNat(z0), x1, x2))) A__U61(tt, U41(U31(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(U41(U31(z0, z1), x1, x2))) A__U61(tt, U41(U32(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U32(mark(z0)), x1, x2)), MARK(U41(U32(z0), x1, x2))) A__U61(tt, U41(U41(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2))) A__U61(tt, U41(U42(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U42(mark(z0), z1), x1, x2)), MARK(U41(U42(z0, z1), x1, x2))) A__U61(tt, U41(U43(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U43(mark(z0)), x1, x2)), MARK(U41(U43(z0), x1, x2))) A__U61(tt, U41(isNatIList(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatIList(z0), x1, x2)), MARK(U41(isNatIList(z0), x1, x2))) A__U61(tt, U41(U51(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U41(a__U51(mark(z0), z1, z2), x1, x2)), MARK(U41(U51(z0, z1, z2), x1, x2))) A__U61(tt, U41(U52(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U52(mark(z0), z1), x1, x2)), MARK(U41(U52(z0, z1), x1, x2))) A__U61(tt, U41(U53(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U53(mark(z0)), x1, x2)), MARK(U41(U53(z0), x1, x2))) A__U61(tt, U41(U61(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U61(mark(z0), z1), x1, x2)), MARK(U41(U61(z0, z1), x1, x2))) A__U61(tt, U41(length(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__length(mark(z0)), x1, x2)), MARK(U41(length(z0), x1, x2))) A__U61(tt, U41(and(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__and(mark(z0), z1), x1, x2)), MARK(U41(and(z0, z1), x1, x2))) A__U61(tt, U41(isNatIListKind(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatIListKind(z0), x1, x2)), MARK(U41(isNatIListKind(z0), x1, x2))) A__U61(tt, U41(isNatKind(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatKind(z0), x1, x2)), MARK(U41(isNatKind(z0), x1, x2))) A__U61(tt, U41(cons(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(cons(mark(z0), z1), x1, x2)), MARK(U41(cons(z0, z1), x1, x2))) A__U61(tt, U41(tt, x1, x2)) -> c26(A__LENGTH(a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2))) A__U61(tt, U41(s(z0), x1, x2)) -> c26(A__LENGTH(a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2))) A__U61(tt, U41(x0, z1, z2)) -> c26(MARK(U41(x0, z1, z2))) A__U61(tt, U41(0, x1, x2)) -> c26(A__LENGTH(a__U41(0, x1, x2))) A__U61(tt, U41(nil, x1, x2)) -> c26(A__LENGTH(a__U41(nil, x1, x2))) A__U61(tt, U42(zeros, x1)) -> c26(A__LENGTH(a__U42(a__zeros, x1)), MARK(U42(zeros, x1))) A__U61(tt, U42(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U11(mark(z0), z1), x1)), MARK(U42(U11(z0, z1), x1))) A__U61(tt, U42(U12(z0), x1)) -> c26(A__LENGTH(a__U42(a__U12(mark(z0)), x1)), MARK(U42(U12(z0), x1))) A__U61(tt, U42(isNatList(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatList(z0), x1)), MARK(U42(isNatList(z0), x1))) A__U61(tt, U42(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U21(mark(z0), z1), x1)), MARK(U42(U21(z0, z1), x1))) A__U61(tt, U42(U22(z0), x1)) -> c26(A__LENGTH(a__U42(a__U22(mark(z0)), x1)), MARK(U42(U22(z0), x1))) A__U61(tt, U42(isNat(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNat(z0), x1)), MARK(U42(isNat(z0), x1))) A__U61(tt, U42(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U31(mark(z0), z1), x1)), MARK(U42(U31(z0, z1), x1))) A__U61(tt, U42(U32(z0), x1)) -> c26(A__LENGTH(a__U42(a__U32(mark(z0)), x1)), MARK(U42(U32(z0), x1))) A__U61(tt, U42(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U42(a__U41(mark(z0), z1, z2), x1)), MARK(U42(U41(z0, z1, z2), x1))) A__U61(tt, U42(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U42(mark(z0), z1), x1)), MARK(U42(U42(z0, z1), x1))) A__U61(tt, U42(U43(z0), x1)) -> c26(A__LENGTH(a__U42(a__U43(mark(z0)), x1)), MARK(U42(U43(z0), x1))) A__U61(tt, U42(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatIList(z0), x1)), MARK(U42(isNatIList(z0), x1))) A__U61(tt, U42(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U42(a__U51(mark(z0), z1, z2), x1)), MARK(U42(U51(z0, z1, z2), x1))) A__U61(tt, U42(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U52(mark(z0), z1), x1)), MARK(U42(U52(z0, z1), x1))) A__U61(tt, U42(U53(z0), x1)) -> c26(A__LENGTH(a__U42(a__U53(mark(z0)), x1)), MARK(U42(U53(z0), x1))) A__U61(tt, U42(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U61(mark(z0), z1), x1)), MARK(U42(U61(z0, z1), x1))) A__U61(tt, U42(length(z0), x1)) -> c26(A__LENGTH(a__U42(a__length(mark(z0)), x1)), MARK(U42(length(z0), x1))) A__U61(tt, U42(and(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__and(mark(z0), z1), x1)), MARK(U42(and(z0, z1), x1))) A__U61(tt, U42(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatIListKind(z0), x1)), MARK(U42(isNatIListKind(z0), x1))) A__U61(tt, U42(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatKind(z0), x1)), MARK(U42(isNatKind(z0), x1))) A__U61(tt, U42(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U42(cons(mark(z0), z1), x1)), MARK(U42(cons(z0, z1), x1))) A__U61(tt, U42(tt, x1)) -> c26(A__LENGTH(a__U42(tt, x1)), MARK(U42(tt, x1))) A__U61(tt, U42(s(z0), x1)) -> c26(A__LENGTH(a__U42(s(mark(z0)), x1)), MARK(U42(s(z0), x1))) A__U61(tt, U42(x0, z1)) -> c26(MARK(U42(x0, z1))) A__U61(tt, U42(0, x1)) -> c26(A__LENGTH(a__U42(0, x1))) A__U61(tt, U42(nil, x1)) -> c26(A__LENGTH(a__U42(nil, x1))) A__U61(tt, U43(zeros)) -> c26(A__LENGTH(a__U43(a__zeros)), MARK(U43(zeros))) A__U61(tt, U43(U11(z0, z1))) -> c26(A__LENGTH(a__U43(a__U11(mark(z0), z1))), MARK(U43(U11(z0, z1)))) A__U61(tt, U43(U12(z0))) -> c26(A__LENGTH(a__U43(a__U12(mark(z0)))), MARK(U43(U12(z0)))) A__U61(tt, U43(isNatList(z0))) -> c26(A__LENGTH(a__U43(a__isNatList(z0))), MARK(U43(isNatList(z0)))) A__U61(tt, U43(U21(z0, z1))) -> c26(A__LENGTH(a__U43(a__U21(mark(z0), z1))), MARK(U43(U21(z0, z1)))) A__U61(tt, U43(U22(z0))) -> c26(A__LENGTH(a__U43(a__U22(mark(z0)))), MARK(U43(U22(z0)))) A__U61(tt, U43(isNat(z0))) -> c26(A__LENGTH(a__U43(a__isNat(z0))), MARK(U43(isNat(z0)))) A__U61(tt, U43(U31(z0, z1))) -> c26(A__LENGTH(a__U43(a__U31(mark(z0), z1))), MARK(U43(U31(z0, z1)))) A__U61(tt, U43(U32(z0))) -> c26(A__LENGTH(a__U43(a__U32(mark(z0)))), MARK(U43(U32(z0)))) A__U61(tt, U43(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U43(a__U41(mark(z0), z1, z2))), MARK(U43(U41(z0, z1, z2)))) A__U61(tt, U43(U42(z0, z1))) -> c26(A__LENGTH(a__U43(a__U42(mark(z0), z1))), MARK(U43(U42(z0, z1)))) A__U61(tt, U43(U43(z0))) -> c26(A__LENGTH(a__U43(a__U43(mark(z0)))), MARK(U43(U43(z0)))) A__U61(tt, U43(isNatIList(z0))) -> c26(A__LENGTH(a__U43(a__isNatIList(z0))), MARK(U43(isNatIList(z0)))) A__U61(tt, U43(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U43(a__U51(mark(z0), z1, z2))), MARK(U43(U51(z0, z1, z2)))) A__U61(tt, U43(U52(z0, z1))) -> c26(A__LENGTH(a__U43(a__U52(mark(z0), z1))), MARK(U43(U52(z0, z1)))) A__U61(tt, U43(U53(z0))) -> c26(A__LENGTH(a__U43(a__U53(mark(z0)))), MARK(U43(U53(z0)))) A__U61(tt, U43(U61(z0, z1))) -> c26(A__LENGTH(a__U43(a__U61(mark(z0), z1))), MARK(U43(U61(z0, z1)))) A__U61(tt, U43(length(z0))) -> c26(A__LENGTH(a__U43(a__length(mark(z0)))), MARK(U43(length(z0)))) A__U61(tt, U43(and(z0, z1))) -> c26(A__LENGTH(a__U43(a__and(mark(z0), z1))), MARK(U43(and(z0, z1)))) A__U61(tt, U43(isNatIListKind(z0))) -> c26(A__LENGTH(a__U43(a__isNatIListKind(z0))), MARK(U43(isNatIListKind(z0)))) A__U61(tt, U43(isNatKind(z0))) -> c26(A__LENGTH(a__U43(a__isNatKind(z0))), MARK(U43(isNatKind(z0)))) A__U61(tt, U43(cons(z0, z1))) -> c26(A__LENGTH(a__U43(cons(mark(z0), z1))), MARK(U43(cons(z0, z1)))) A__U61(tt, U43(0)) -> c26(A__LENGTH(a__U43(0)), MARK(U43(0))) A__U61(tt, U43(tt)) -> c26(A__LENGTH(a__U43(tt)), MARK(U43(tt))) A__U61(tt, U43(s(z0))) -> c26(A__LENGTH(a__U43(s(mark(z0)))), MARK(U43(s(z0)))) A__U61(tt, U43(nil)) -> c26(A__LENGTH(a__U43(nil)), MARK(U43(nil))) A__U61(tt, U43(x0)) -> c26(MARK(U43(x0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__U31(a__isNatIListKind(z0), z0)), MARK(isNatIList(z0))) A__U61(tt, isNatIList(cons(z0, z1))) -> c26(A__LENGTH(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatIList(cons(z0, z1)))) A__U61(tt, isNatIList(zeros)) -> c26(MARK(isNatIList(zeros))) A__U61(tt, isNatIList(z0)) -> c26(MARK(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_1, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c14_2, c20_2 ---------------------------------------- (195) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U61(tt, U51(z0, z1, z2)) -> c26(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) by A__U61(tt, U51(x0, z1, z2)) -> c26(A__LENGTH(U51(mark(x0), z1, z2)), MARK(U51(x0, z1, z2))) A__U61(tt, U51(zeros, x1, x2)) -> c26(A__LENGTH(a__U51(a__zeros, x1, x2)), MARK(U51(zeros, x1, x2))) A__U61(tt, U51(U11(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U11(mark(z0), z1), x1, x2)), MARK(U51(U11(z0, z1), x1, x2))) A__U61(tt, U51(U12(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U12(mark(z0)), x1, x2)), MARK(U51(U12(z0), x1, x2))) A__U61(tt, U51(isNatList(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatList(z0), x1, x2)), MARK(U51(isNatList(z0), x1, x2))) A__U61(tt, U51(U21(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U21(mark(z0), z1), x1, x2)), MARK(U51(U21(z0, z1), x1, x2))) A__U61(tt, U51(U22(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U22(mark(z0)), x1, x2)), MARK(U51(U22(z0), x1, x2))) A__U61(tt, U51(isNat(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNat(z0), x1, x2)), MARK(U51(isNat(z0), x1, x2))) A__U61(tt, U51(U31(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U31(mark(z0), z1), x1, x2)), MARK(U51(U31(z0, z1), x1, x2))) A__U61(tt, U51(U32(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U32(mark(z0)), x1, x2)), MARK(U51(U32(z0), x1, x2))) A__U61(tt, U51(U41(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U51(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U51(U41(z0, z1, z2), x1, x2))) A__U61(tt, U51(U42(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U42(mark(z0), z1), x1, x2)), MARK(U51(U42(z0, z1), x1, x2))) A__U61(tt, U51(U43(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U43(mark(z0)), x1, x2)), MARK(U51(U43(z0), x1, x2))) A__U61(tt, U51(isNatIList(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatIList(z0), x1, x2)), MARK(U51(isNatIList(z0), x1, x2))) A__U61(tt, U51(U51(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U51(a__U51(mark(z0), z1, z2), x1, x2)), MARK(U51(U51(z0, z1, z2), x1, x2))) A__U61(tt, U51(U52(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U52(mark(z0), z1), x1, x2)), MARK(U51(U52(z0, z1), x1, x2))) A__U61(tt, U51(U53(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U53(mark(z0)), x1, x2)), MARK(U51(U53(z0), x1, x2))) A__U61(tt, U51(U61(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U61(mark(z0), z1), x1, x2)), MARK(U51(U61(z0, z1), x1, x2))) A__U61(tt, U51(length(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__length(mark(z0)), x1, x2)), MARK(U51(length(z0), x1, x2))) A__U61(tt, U51(and(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__and(mark(z0), z1), x1, x2)), MARK(U51(and(z0, z1), x1, x2))) A__U61(tt, U51(isNatIListKind(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatIListKind(z0), x1, x2)), MARK(U51(isNatIListKind(z0), x1, x2))) A__U61(tt, U51(isNatKind(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatKind(z0), x1, x2)), MARK(U51(isNatKind(z0), x1, x2))) A__U61(tt, U51(cons(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(cons(mark(z0), z1), x1, x2)), MARK(U51(cons(z0, z1), x1, x2))) A__U61(tt, U51(0, x1, x2)) -> c26(A__LENGTH(a__U51(0, x1, x2)), MARK(U51(0, x1, x2))) A__U61(tt, U51(tt, x1, x2)) -> c26(A__LENGTH(a__U51(tt, x1, x2)), MARK(U51(tt, x1, x2))) A__U61(tt, U51(s(z0), x1, x2)) -> c26(A__LENGTH(a__U51(s(mark(z0)), x1, x2)), MARK(U51(s(z0), x1, x2))) A__U61(tt, U51(nil, x1, x2)) -> c26(A__LENGTH(a__U51(nil, x1, x2)), MARK(U51(nil, x1, x2))) ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), 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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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> c26(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U61(tt, U12(U21(z0, z1))) -> c26(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U61(tt, U12(U22(z0))) -> 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A__U61(tt, isNatList(cons(z0, z1))) -> c26(A__LENGTH(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(cons(z0, z1)))) A__U61(tt, isNatList(nil)) -> c26(MARK(isNatList(nil))) A__U61(tt, isNatList(z0)) -> c26(MARK(isNatList(z0))) A__U61(tt, U21(zeros, x1)) -> c26(A__LENGTH(a__U21(a__zeros, x1)), MARK(U21(zeros, x1))) A__U61(tt, U21(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1)), MARK(U21(U11(z0, z1), x1))) A__U61(tt, U21(U12(z0), x1)) -> c26(A__LENGTH(a__U21(a__U12(mark(z0)), x1)), MARK(U21(U12(z0), x1))) A__U61(tt, U21(isNatList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatList(z0), x1)), MARK(U21(isNatList(z0), x1))) A__U61(tt, U21(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U21(mark(z0), z1), x1)), MARK(U21(U21(z0, z1), x1))) A__U61(tt, U21(U22(z0), x1)) -> c26(A__LENGTH(a__U21(a__U22(mark(z0)), x1)), MARK(U21(U22(z0), x1))) A__U61(tt, U21(isNat(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNat(z0), x1)), MARK(U21(isNat(z0), x1))) A__U61(tt, 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A__U61(tt, U41(s(z0), x1, x2)) -> c26(A__LENGTH(a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2))) A__U61(tt, U41(x0, z1, z2)) -> c26(MARK(U41(x0, z1, z2))) A__U61(tt, U41(0, x1, x2)) -> c26(A__LENGTH(a__U41(0, x1, x2))) A__U61(tt, U41(nil, x1, x2)) -> c26(A__LENGTH(a__U41(nil, x1, x2))) A__U61(tt, U42(zeros, x1)) -> c26(A__LENGTH(a__U42(a__zeros, x1)), MARK(U42(zeros, x1))) A__U61(tt, U42(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U11(mark(z0), z1), x1)), MARK(U42(U11(z0, z1), x1))) A__U61(tt, U42(U12(z0), x1)) -> c26(A__LENGTH(a__U42(a__U12(mark(z0)), x1)), MARK(U42(U12(z0), x1))) A__U61(tt, U42(isNatList(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatList(z0), x1)), MARK(U42(isNatList(z0), x1))) A__U61(tt, U42(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U21(mark(z0), z1), x1)), MARK(U42(U21(z0, z1), x1))) A__U61(tt, U42(U22(z0), x1)) -> c26(A__LENGTH(a__U42(a__U22(mark(z0)), x1)), MARK(U42(U22(z0), x1))) A__U61(tt, U42(isNat(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNat(z0), x1)), MARK(U42(isNat(z0), x1))) A__U61(tt, U42(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U31(mark(z0), z1), x1)), MARK(U42(U31(z0, z1), x1))) A__U61(tt, U42(U32(z0), x1)) -> c26(A__LENGTH(a__U42(a__U32(mark(z0)), x1)), MARK(U42(U32(z0), x1))) A__U61(tt, U42(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U42(a__U41(mark(z0), z1, z2), x1)), MARK(U42(U41(z0, z1, z2), x1))) A__U61(tt, U42(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U42(mark(z0), z1), x1)), MARK(U42(U42(z0, z1), x1))) A__U61(tt, U42(U43(z0), x1)) -> c26(A__LENGTH(a__U42(a__U43(mark(z0)), x1)), MARK(U42(U43(z0), x1))) A__U61(tt, U42(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatIList(z0), x1)), MARK(U42(isNatIList(z0), x1))) A__U61(tt, U42(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U42(a__U51(mark(z0), z1, z2), x1)), MARK(U42(U51(z0, z1, z2), x1))) A__U61(tt, U42(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U52(mark(z0), z1), x1)), MARK(U42(U52(z0, z1), x1))) A__U61(tt, U42(U53(z0), x1)) -> c26(A__LENGTH(a__U42(a__U53(mark(z0)), x1)), MARK(U42(U53(z0), x1))) A__U61(tt, U42(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U61(mark(z0), z1), x1)), MARK(U42(U61(z0, z1), x1))) A__U61(tt, U42(length(z0), x1)) -> c26(A__LENGTH(a__U42(a__length(mark(z0)), x1)), MARK(U42(length(z0), x1))) A__U61(tt, U42(and(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__and(mark(z0), z1), x1)), MARK(U42(and(z0, z1), x1))) A__U61(tt, U42(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatIListKind(z0), x1)), MARK(U42(isNatIListKind(z0), x1))) A__U61(tt, U42(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatKind(z0), x1)), MARK(U42(isNatKind(z0), x1))) A__U61(tt, U42(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U42(cons(mark(z0), z1), x1)), MARK(U42(cons(z0, z1), x1))) A__U61(tt, U42(tt, x1)) -> c26(A__LENGTH(a__U42(tt, x1)), MARK(U42(tt, x1))) A__U61(tt, U42(s(z0), x1)) -> c26(A__LENGTH(a__U42(s(mark(z0)), x1)), MARK(U42(s(z0), x1))) A__U61(tt, U42(x0, z1)) -> c26(MARK(U42(x0, z1))) A__U61(tt, U42(0, x1)) -> c26(A__LENGTH(a__U42(0, x1))) A__U61(tt, U42(nil, x1)) -> c26(A__LENGTH(a__U42(nil, x1))) A__U61(tt, U43(zeros)) -> c26(A__LENGTH(a__U43(a__zeros)), MARK(U43(zeros))) A__U61(tt, U43(U11(z0, z1))) -> c26(A__LENGTH(a__U43(a__U11(mark(z0), z1))), MARK(U43(U11(z0, z1)))) A__U61(tt, U43(U12(z0))) -> c26(A__LENGTH(a__U43(a__U12(mark(z0)))), MARK(U43(U12(z0)))) A__U61(tt, U43(isNatList(z0))) -> c26(A__LENGTH(a__U43(a__isNatList(z0))), MARK(U43(isNatList(z0)))) A__U61(tt, U43(U21(z0, z1))) -> c26(A__LENGTH(a__U43(a__U21(mark(z0), z1))), MARK(U43(U21(z0, z1)))) A__U61(tt, U43(U22(z0))) -> c26(A__LENGTH(a__U43(a__U22(mark(z0)))), MARK(U43(U22(z0)))) A__U61(tt, U43(isNat(z0))) -> c26(A__LENGTH(a__U43(a__isNat(z0))), MARK(U43(isNat(z0)))) A__U61(tt, U43(U31(z0, z1))) -> c26(A__LENGTH(a__U43(a__U31(mark(z0), z1))), MARK(U43(U31(z0, z1)))) A__U61(tt, U43(U32(z0))) -> c26(A__LENGTH(a__U43(a__U32(mark(z0)))), MARK(U43(U32(z0)))) A__U61(tt, U43(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U43(a__U41(mark(z0), z1, z2))), MARK(U43(U41(z0, z1, z2)))) A__U61(tt, U43(U42(z0, z1))) -> c26(A__LENGTH(a__U43(a__U42(mark(z0), z1))), MARK(U43(U42(z0, z1)))) A__U61(tt, U43(U43(z0))) -> c26(A__LENGTH(a__U43(a__U43(mark(z0)))), MARK(U43(U43(z0)))) A__U61(tt, U43(isNatIList(z0))) -> c26(A__LENGTH(a__U43(a__isNatIList(z0))), MARK(U43(isNatIList(z0)))) A__U61(tt, U43(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U43(a__U51(mark(z0), z1, z2))), MARK(U43(U51(z0, z1, z2)))) A__U61(tt, U43(U52(z0, z1))) -> c26(A__LENGTH(a__U43(a__U52(mark(z0), z1))), MARK(U43(U52(z0, z1)))) A__U61(tt, U43(U53(z0))) -> c26(A__LENGTH(a__U43(a__U53(mark(z0)))), MARK(U43(U53(z0)))) A__U61(tt, U43(U61(z0, z1))) -> c26(A__LENGTH(a__U43(a__U61(mark(z0), z1))), MARK(U43(U61(z0, z1)))) A__U61(tt, U43(length(z0))) -> c26(A__LENGTH(a__U43(a__length(mark(z0)))), MARK(U43(length(z0)))) A__U61(tt, U43(and(z0, z1))) -> c26(A__LENGTH(a__U43(a__and(mark(z0), z1))), MARK(U43(and(z0, z1)))) A__U61(tt, U43(isNatIListKind(z0))) -> c26(A__LENGTH(a__U43(a__isNatIListKind(z0))), MARK(U43(isNatIListKind(z0)))) A__U61(tt, U43(isNatKind(z0))) -> c26(A__LENGTH(a__U43(a__isNatKind(z0))), MARK(U43(isNatKind(z0)))) A__U61(tt, U43(cons(z0, z1))) -> c26(A__LENGTH(a__U43(cons(mark(z0), z1))), MARK(U43(cons(z0, z1)))) A__U61(tt, U43(0)) -> c26(A__LENGTH(a__U43(0)), MARK(U43(0))) A__U61(tt, U43(tt)) -> c26(A__LENGTH(a__U43(tt)), MARK(U43(tt))) A__U61(tt, U43(s(z0))) -> c26(A__LENGTH(a__U43(s(mark(z0)))), MARK(U43(s(z0)))) A__U61(tt, U43(nil)) -> c26(A__LENGTH(a__U43(nil)), MARK(U43(nil))) A__U61(tt, U43(x0)) -> c26(MARK(U43(x0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__U31(a__isNatIListKind(z0), z0)), MARK(isNatIList(z0))) A__U61(tt, isNatIList(cons(z0, z1))) -> c26(A__LENGTH(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatIList(cons(z0, z1)))) A__U61(tt, isNatIList(zeros)) -> c26(MARK(isNatIList(zeros))) A__U61(tt, isNatIList(z0)) -> c26(MARK(isNatIList(z0))) A__U61(tt, U51(x0, z1, z2)) -> c26(A__LENGTH(U51(mark(x0), z1, z2)), MARK(U51(x0, z1, z2))) A__U61(tt, U51(zeros, x1, x2)) -> c26(A__LENGTH(a__U51(a__zeros, x1, x2)), MARK(U51(zeros, x1, x2))) A__U61(tt, U51(U11(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U11(mark(z0), z1), x1, x2)), MARK(U51(U11(z0, z1), x1, x2))) A__U61(tt, U51(U12(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U12(mark(z0)), x1, x2)), MARK(U51(U12(z0), x1, x2))) A__U61(tt, U51(isNatList(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatList(z0), x1, x2)), MARK(U51(isNatList(z0), x1, x2))) A__U61(tt, U51(U21(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U21(mark(z0), z1), x1, x2)), MARK(U51(U21(z0, z1), x1, x2))) A__U61(tt, U51(U22(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U22(mark(z0)), x1, x2)), MARK(U51(U22(z0), x1, x2))) A__U61(tt, U51(isNat(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNat(z0), x1, x2)), MARK(U51(isNat(z0), x1, x2))) A__U61(tt, U51(U31(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U31(mark(z0), z1), x1, x2)), MARK(U51(U31(z0, z1), x1, x2))) A__U61(tt, U51(U32(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U32(mark(z0)), x1, x2)), MARK(U51(U32(z0), x1, x2))) A__U61(tt, U51(U41(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U51(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U51(U41(z0, z1, z2), x1, x2))) A__U61(tt, U51(U42(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U42(mark(z0), z1), x1, x2)), MARK(U51(U42(z0, z1), x1, x2))) A__U61(tt, U51(U43(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U43(mark(z0)), x1, x2)), MARK(U51(U43(z0), x1, x2))) A__U61(tt, U51(isNatIList(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatIList(z0), x1, x2)), MARK(U51(isNatIList(z0), x1, x2))) A__U61(tt, U51(U51(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U51(a__U51(mark(z0), z1, z2), x1, x2)), MARK(U51(U51(z0, z1, z2), x1, x2))) A__U61(tt, U51(U52(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U52(mark(z0), z1), x1, x2)), MARK(U51(U52(z0, z1), x1, x2))) A__U61(tt, U51(U53(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U53(mark(z0)), x1, x2)), MARK(U51(U53(z0), x1, x2))) A__U61(tt, U51(U61(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U61(mark(z0), z1), x1, x2)), MARK(U51(U61(z0, z1), x1, x2))) A__U61(tt, U51(length(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__length(mark(z0)), x1, x2)), MARK(U51(length(z0), x1, x2))) A__U61(tt, U51(and(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__and(mark(z0), z1), x1, x2)), MARK(U51(and(z0, z1), x1, x2))) A__U61(tt, U51(isNatIListKind(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatIListKind(z0), x1, x2)), MARK(U51(isNatIListKind(z0), x1, x2))) A__U61(tt, U51(isNatKind(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatKind(z0), x1, x2)), MARK(U51(isNatKind(z0), x1, x2))) A__U61(tt, U51(cons(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(cons(mark(z0), z1), x1, x2)), MARK(U51(cons(z0, z1), x1, x2))) A__U61(tt, U51(0, x1, x2)) -> c26(A__LENGTH(a__U51(0, x1, x2)), MARK(U51(0, x1, x2))) A__U61(tt, U51(tt, x1, x2)) -> c26(A__LENGTH(a__U51(tt, x1, x2)), MARK(U51(tt, x1, x2))) A__U61(tt, U51(s(z0), x1, x2)) -> c26(A__LENGTH(a__U51(s(mark(z0)), x1, x2)), MARK(U51(s(z0), x1, x2))) A__U61(tt, U51(nil, x1, x2)) -> c26(A__LENGTH(a__U51(nil, x1, x2)), MARK(U51(nil, x1, x2))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) 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MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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), 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c26(A__LENGTH(a__U31(a__U53(mark(z0)), x1)), MARK(U31(U53(z0), x1))) A__U61(tt, U31(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U61(mark(z0), z1), x1)), MARK(U31(U61(z0, z1), x1))) A__U61(tt, U31(length(z0), x1)) -> c26(A__LENGTH(a__U31(a__length(mark(z0)), x1)), MARK(U31(length(z0), x1))) A__U61(tt, U31(and(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__and(mark(z0), z1), x1)), MARK(U31(and(z0, z1), x1))) A__U61(tt, U31(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatIListKind(z0), x1)), MARK(U31(isNatIListKind(z0), x1))) A__U61(tt, U31(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatKind(z0), x1)), MARK(U31(isNatKind(z0), x1))) A__U61(tt, U31(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U31(cons(mark(z0), z1), x1)), MARK(U31(cons(z0, z1), x1))) A__U61(tt, U31(tt, x1)) -> c26(A__LENGTH(a__U31(tt, x1)), MARK(U31(tt, x1))) A__U61(tt, U31(s(z0), x1)) -> c26(A__LENGTH(a__U31(s(mark(z0)), x1)), MARK(U31(s(z0), x1))) A__U61(tt, U31(x0, z1)) -> c26(MARK(U31(x0, z1))) A__U61(tt, U31(0, x1)) -> c26(A__LENGTH(a__U31(0, x1))) A__U61(tt, U31(nil, x1)) -> c26(A__LENGTH(a__U31(nil, x1))) A__U61(tt, U32(zeros)) -> c26(A__LENGTH(a__U32(a__zeros)), MARK(U32(zeros))) A__U61(tt, U32(U11(z0, z1))) -> c26(A__LENGTH(a__U32(a__U11(mark(z0), z1))), MARK(U32(U11(z0, z1)))) A__U61(tt, U32(U12(z0))) -> c26(A__LENGTH(a__U32(a__U12(mark(z0)))), MARK(U32(U12(z0)))) A__U61(tt, U32(isNatList(z0))) -> c26(A__LENGTH(a__U32(a__isNatList(z0))), MARK(U32(isNatList(z0)))) A__U61(tt, U32(U21(z0, z1))) -> c26(A__LENGTH(a__U32(a__U21(mark(z0), z1))), MARK(U32(U21(z0, z1)))) A__U61(tt, U32(U22(z0))) -> c26(A__LENGTH(a__U32(a__U22(mark(z0)))), MARK(U32(U22(z0)))) A__U61(tt, U32(isNat(z0))) -> c26(A__LENGTH(a__U32(a__isNat(z0))), MARK(U32(isNat(z0)))) A__U61(tt, U32(U31(z0, z1))) -> c26(A__LENGTH(a__U32(a__U31(mark(z0), z1))), MARK(U32(U31(z0, z1)))) A__U61(tt, U32(U32(z0))) -> c26(A__LENGTH(a__U32(a__U32(mark(z0)))), MARK(U32(U32(z0)))) A__U61(tt, U32(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U32(a__U41(mark(z0), z1, z2))), MARK(U32(U41(z0, z1, z2)))) A__U61(tt, U32(U42(z0, z1))) -> c26(A__LENGTH(a__U32(a__U42(mark(z0), z1))), MARK(U32(U42(z0, z1)))) A__U61(tt, U32(U43(z0))) -> c26(A__LENGTH(a__U32(a__U43(mark(z0)))), MARK(U32(U43(z0)))) A__U61(tt, U32(isNatIList(z0))) -> c26(A__LENGTH(a__U32(a__isNatIList(z0))), MARK(U32(isNatIList(z0)))) A__U61(tt, U32(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U32(a__U51(mark(z0), z1, z2))), MARK(U32(U51(z0, z1, z2)))) A__U61(tt, U32(U52(z0, z1))) -> c26(A__LENGTH(a__U32(a__U52(mark(z0), z1))), MARK(U32(U52(z0, z1)))) A__U61(tt, U32(U53(z0))) -> c26(A__LENGTH(a__U32(a__U53(mark(z0)))), MARK(U32(U53(z0)))) A__U61(tt, U32(U61(z0, z1))) -> c26(A__LENGTH(a__U32(a__U61(mark(z0), z1))), MARK(U32(U61(z0, z1)))) A__U61(tt, U32(length(z0))) -> c26(A__LENGTH(a__U32(a__length(mark(z0)))), MARK(U32(length(z0)))) A__U61(tt, U32(and(z0, z1))) -> c26(A__LENGTH(a__U32(a__and(mark(z0), z1))), MARK(U32(and(z0, z1)))) A__U61(tt, U32(isNatIListKind(z0))) -> c26(A__LENGTH(a__U32(a__isNatIListKind(z0))), MARK(U32(isNatIListKind(z0)))) A__U61(tt, U32(isNatKind(z0))) -> c26(A__LENGTH(a__U32(a__isNatKind(z0))), MARK(U32(isNatKind(z0)))) A__U61(tt, U32(cons(z0, z1))) -> c26(A__LENGTH(a__U32(cons(mark(z0), z1))), MARK(U32(cons(z0, z1)))) A__U61(tt, U32(0)) -> c26(A__LENGTH(a__U32(0)), MARK(U32(0))) A__U61(tt, U32(tt)) -> c26(A__LENGTH(a__U32(tt)), MARK(U32(tt))) A__U61(tt, U32(s(z0))) -> c26(A__LENGTH(a__U32(s(mark(z0)))), MARK(U32(s(z0)))) A__U61(tt, U32(nil)) -> c26(A__LENGTH(a__U32(nil)), MARK(U32(nil))) A__U61(tt, U32(x0)) -> c26(MARK(U32(x0))) A__U61(tt, U41(zeros, x1, x2)) -> c26(A__LENGTH(a__U41(a__zeros, x1, x2)), MARK(U41(zeros, x1, x2))) A__U61(tt, U41(U11(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(U41(U11(z0, z1), x1, x2))) A__U61(tt, U41(U12(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U12(mark(z0)), x1, x2)), MARK(U41(U12(z0), x1, x2))) A__U61(tt, U41(isNatList(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatList(z0), x1, x2)), MARK(U41(isNatList(z0), x1, x2))) A__U61(tt, U41(U21(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U21(mark(z0), z1), x1, x2)), MARK(U41(U21(z0, z1), x1, x2))) A__U61(tt, U41(U22(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U22(mark(z0)), x1, x2)), MARK(U41(U22(z0), x1, x2))) A__U61(tt, U41(isNat(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNat(z0), x1, x2)), MARK(U41(isNat(z0), x1, x2))) A__U61(tt, U41(U31(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(U41(U31(z0, z1), x1, x2))) A__U61(tt, U41(U32(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U32(mark(z0)), x1, x2)), MARK(U41(U32(z0), x1, x2))) A__U61(tt, U41(U41(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2))) A__U61(tt, U41(U42(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U42(mark(z0), z1), x1, x2)), MARK(U41(U42(z0, z1), x1, x2))) A__U61(tt, U41(U43(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U43(mark(z0)), x1, x2)), MARK(U41(U43(z0), x1, x2))) A__U61(tt, U41(isNatIList(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatIList(z0), x1, x2)), MARK(U41(isNatIList(z0), x1, x2))) A__U61(tt, U41(U51(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U41(a__U51(mark(z0), z1, z2), x1, x2)), MARK(U41(U51(z0, z1, z2), x1, x2))) A__U61(tt, U41(U52(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U52(mark(z0), z1), x1, x2)), MARK(U41(U52(z0, z1), x1, x2))) A__U61(tt, U41(U53(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U53(mark(z0)), x1, x2)), MARK(U41(U53(z0), x1, x2))) A__U61(tt, U41(U61(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U61(mark(z0), z1), x1, x2)), MARK(U41(U61(z0, z1), x1, x2))) A__U61(tt, U41(length(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__length(mark(z0)), x1, x2)), MARK(U41(length(z0), x1, x2))) A__U61(tt, U41(and(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__and(mark(z0), z1), x1, x2)), MARK(U41(and(z0, z1), x1, x2))) A__U61(tt, U41(isNatIListKind(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatIListKind(z0), x1, x2)), MARK(U41(isNatIListKind(z0), x1, x2))) A__U61(tt, U41(isNatKind(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatKind(z0), x1, x2)), MARK(U41(isNatKind(z0), x1, x2))) A__U61(tt, U41(cons(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(cons(mark(z0), z1), x1, x2)), MARK(U41(cons(z0, z1), x1, x2))) A__U61(tt, U41(tt, x1, x2)) -> c26(A__LENGTH(a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2))) A__U61(tt, U41(s(z0), x1, x2)) -> c26(A__LENGTH(a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2))) A__U61(tt, U41(x0, z1, z2)) -> c26(MARK(U41(x0, z1, z2))) A__U61(tt, U41(0, x1, x2)) -> c26(A__LENGTH(a__U41(0, x1, x2))) A__U61(tt, U41(nil, x1, x2)) -> c26(A__LENGTH(a__U41(nil, x1, x2))) A__U61(tt, U42(zeros, x1)) -> c26(A__LENGTH(a__U42(a__zeros, x1)), MARK(U42(zeros, x1))) A__U61(tt, U42(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U11(mark(z0), z1), x1)), MARK(U42(U11(z0, z1), x1))) A__U61(tt, U42(U12(z0), x1)) -> c26(A__LENGTH(a__U42(a__U12(mark(z0)), x1)), MARK(U42(U12(z0), x1))) A__U61(tt, U42(isNatList(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatList(z0), x1)), MARK(U42(isNatList(z0), x1))) A__U61(tt, U42(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U21(mark(z0), z1), x1)), MARK(U42(U21(z0, z1), x1))) A__U61(tt, U42(U22(z0), x1)) -> c26(A__LENGTH(a__U42(a__U22(mark(z0)), x1)), MARK(U42(U22(z0), x1))) A__U61(tt, U42(isNat(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNat(z0), x1)), MARK(U42(isNat(z0), x1))) A__U61(tt, U42(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U31(mark(z0), z1), x1)), MARK(U42(U31(z0, z1), x1))) A__U61(tt, U42(U32(z0), x1)) -> c26(A__LENGTH(a__U42(a__U32(mark(z0)), x1)), MARK(U42(U32(z0), x1))) A__U61(tt, U42(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U42(a__U41(mark(z0), z1, z2), x1)), MARK(U42(U41(z0, z1, z2), x1))) A__U61(tt, U42(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U42(mark(z0), z1), x1)), MARK(U42(U42(z0, z1), x1))) A__U61(tt, U42(U43(z0), x1)) -> c26(A__LENGTH(a__U42(a__U43(mark(z0)), x1)), MARK(U42(U43(z0), x1))) A__U61(tt, U42(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatIList(z0), x1)), MARK(U42(isNatIList(z0), x1))) A__U61(tt, U42(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U42(a__U51(mark(z0), z1, z2), x1)), MARK(U42(U51(z0, z1, z2), x1))) A__U61(tt, U42(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U52(mark(z0), z1), x1)), MARK(U42(U52(z0, z1), x1))) A__U61(tt, U42(U53(z0), x1)) -> c26(A__LENGTH(a__U42(a__U53(mark(z0)), x1)), MARK(U42(U53(z0), x1))) A__U61(tt, U42(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U61(mark(z0), z1), x1)), MARK(U42(U61(z0, z1), x1))) A__U61(tt, U42(length(z0), x1)) -> c26(A__LENGTH(a__U42(a__length(mark(z0)), x1)), MARK(U42(length(z0), x1))) A__U61(tt, U42(and(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__and(mark(z0), z1), x1)), MARK(U42(and(z0, z1), x1))) A__U61(tt, U42(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatIListKind(z0), x1)), MARK(U42(isNatIListKind(z0), x1))) A__U61(tt, U42(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatKind(z0), x1)), MARK(U42(isNatKind(z0), x1))) A__U61(tt, U42(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U42(cons(mark(z0), z1), x1)), MARK(U42(cons(z0, z1), x1))) A__U61(tt, U42(tt, x1)) -> c26(A__LENGTH(a__U42(tt, x1)), MARK(U42(tt, x1))) A__U61(tt, U42(s(z0), x1)) -> c26(A__LENGTH(a__U42(s(mark(z0)), x1)), MARK(U42(s(z0), x1))) A__U61(tt, U42(x0, z1)) -> c26(MARK(U42(x0, z1))) A__U61(tt, U42(0, x1)) -> c26(A__LENGTH(a__U42(0, x1))) A__U61(tt, U42(nil, x1)) -> c26(A__LENGTH(a__U42(nil, x1))) A__U61(tt, U43(zeros)) -> c26(A__LENGTH(a__U43(a__zeros)), MARK(U43(zeros))) A__U61(tt, U43(U11(z0, z1))) -> c26(A__LENGTH(a__U43(a__U11(mark(z0), z1))), MARK(U43(U11(z0, z1)))) A__U61(tt, U43(U12(z0))) -> c26(A__LENGTH(a__U43(a__U12(mark(z0)))), MARK(U43(U12(z0)))) A__U61(tt, U43(isNatList(z0))) -> c26(A__LENGTH(a__U43(a__isNatList(z0))), MARK(U43(isNatList(z0)))) A__U61(tt, U43(U21(z0, z1))) -> c26(A__LENGTH(a__U43(a__U21(mark(z0), z1))), MARK(U43(U21(z0, z1)))) A__U61(tt, U43(U22(z0))) -> c26(A__LENGTH(a__U43(a__U22(mark(z0)))), MARK(U43(U22(z0)))) A__U61(tt, U43(isNat(z0))) -> c26(A__LENGTH(a__U43(a__isNat(z0))), MARK(U43(isNat(z0)))) A__U61(tt, U43(U31(z0, z1))) -> c26(A__LENGTH(a__U43(a__U31(mark(z0), z1))), MARK(U43(U31(z0, z1)))) A__U61(tt, U43(U32(z0))) -> c26(A__LENGTH(a__U43(a__U32(mark(z0)))), MARK(U43(U32(z0)))) A__U61(tt, U43(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U43(a__U41(mark(z0), z1, z2))), MARK(U43(U41(z0, z1, z2)))) A__U61(tt, U43(U42(z0, z1))) -> c26(A__LENGTH(a__U43(a__U42(mark(z0), z1))), MARK(U43(U42(z0, z1)))) A__U61(tt, U43(U43(z0))) -> c26(A__LENGTH(a__U43(a__U43(mark(z0)))), MARK(U43(U43(z0)))) A__U61(tt, U43(isNatIList(z0))) -> c26(A__LENGTH(a__U43(a__isNatIList(z0))), MARK(U43(isNatIList(z0)))) A__U61(tt, U43(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U43(a__U51(mark(z0), z1, z2))), MARK(U43(U51(z0, z1, z2)))) A__U61(tt, U43(U52(z0, z1))) -> c26(A__LENGTH(a__U43(a__U52(mark(z0), z1))), MARK(U43(U52(z0, z1)))) A__U61(tt, U43(U53(z0))) -> c26(A__LENGTH(a__U43(a__U53(mark(z0)))), MARK(U43(U53(z0)))) A__U61(tt, U43(U61(z0, z1))) -> c26(A__LENGTH(a__U43(a__U61(mark(z0), z1))), MARK(U43(U61(z0, z1)))) A__U61(tt, U43(length(z0))) -> c26(A__LENGTH(a__U43(a__length(mark(z0)))), MARK(U43(length(z0)))) A__U61(tt, U43(and(z0, z1))) -> c26(A__LENGTH(a__U43(a__and(mark(z0), z1))), MARK(U43(and(z0, z1)))) A__U61(tt, U43(isNatIListKind(z0))) -> c26(A__LENGTH(a__U43(a__isNatIListKind(z0))), MARK(U43(isNatIListKind(z0)))) A__U61(tt, U43(isNatKind(z0))) -> c26(A__LENGTH(a__U43(a__isNatKind(z0))), MARK(U43(isNatKind(z0)))) A__U61(tt, U43(cons(z0, z1))) -> c26(A__LENGTH(a__U43(cons(mark(z0), z1))), MARK(U43(cons(z0, z1)))) A__U61(tt, U43(0)) -> c26(A__LENGTH(a__U43(0)), MARK(U43(0))) A__U61(tt, U43(tt)) -> c26(A__LENGTH(a__U43(tt)), MARK(U43(tt))) A__U61(tt, U43(s(z0))) -> c26(A__LENGTH(a__U43(s(mark(z0)))), MARK(U43(s(z0)))) A__U61(tt, U43(nil)) -> c26(A__LENGTH(a__U43(nil)), MARK(U43(nil))) A__U61(tt, U43(x0)) -> c26(MARK(U43(x0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__U31(a__isNatIListKind(z0), z0)), MARK(isNatIList(z0))) A__U61(tt, isNatIList(cons(z0, z1))) -> c26(A__LENGTH(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatIList(cons(z0, z1)))) A__U61(tt, isNatIList(zeros)) -> c26(MARK(isNatIList(zeros))) A__U61(tt, isNatIList(z0)) -> c26(MARK(isNatIList(z0))) A__U61(tt, U51(x0, z1, z2)) -> c26(A__LENGTH(U51(mark(x0), z1, z2)), MARK(U51(x0, z1, z2))) A__U61(tt, U51(zeros, x1, x2)) -> c26(A__LENGTH(a__U51(a__zeros, x1, x2)), MARK(U51(zeros, x1, x2))) A__U61(tt, U51(U11(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U11(mark(z0), z1), x1, x2)), MARK(U51(U11(z0, z1), x1, x2))) A__U61(tt, U51(U12(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U12(mark(z0)), x1, x2)), MARK(U51(U12(z0), x1, x2))) A__U61(tt, U51(isNatList(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatList(z0), x1, x2)), MARK(U51(isNatList(z0), x1, x2))) A__U61(tt, U51(U21(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U21(mark(z0), z1), x1, x2)), MARK(U51(U21(z0, z1), x1, x2))) A__U61(tt, U51(U22(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U22(mark(z0)), x1, x2)), MARK(U51(U22(z0), x1, x2))) A__U61(tt, U51(isNat(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNat(z0), x1, x2)), MARK(U51(isNat(z0), x1, x2))) A__U61(tt, U51(U31(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U31(mark(z0), z1), x1, x2)), MARK(U51(U31(z0, z1), x1, x2))) A__U61(tt, U51(U32(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U32(mark(z0)), x1, x2)), MARK(U51(U32(z0), x1, x2))) A__U61(tt, U51(U41(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U51(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U51(U41(z0, z1, z2), x1, x2))) A__U61(tt, U51(U42(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U42(mark(z0), z1), x1, x2)), MARK(U51(U42(z0, z1), x1, x2))) A__U61(tt, U51(U43(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U43(mark(z0)), x1, x2)), MARK(U51(U43(z0), x1, x2))) A__U61(tt, U51(isNatIList(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatIList(z0), x1, x2)), MARK(U51(isNatIList(z0), x1, x2))) A__U61(tt, U51(U51(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U51(a__U51(mark(z0), z1, z2), x1, x2)), MARK(U51(U51(z0, z1, z2), x1, x2))) A__U61(tt, U51(U52(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U52(mark(z0), z1), x1, x2)), MARK(U51(U52(z0, z1), x1, x2))) A__U61(tt, U51(U53(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U53(mark(z0)), x1, x2)), MARK(U51(U53(z0), x1, x2))) A__U61(tt, U51(U61(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U61(mark(z0), z1), x1, x2)), MARK(U51(U61(z0, z1), x1, x2))) A__U61(tt, U51(length(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__length(mark(z0)), x1, x2)), MARK(U51(length(z0), x1, x2))) A__U61(tt, U51(and(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__and(mark(z0), z1), x1, x2)), MARK(U51(and(z0, z1), x1, x2))) A__U61(tt, U51(isNatIListKind(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatIListKind(z0), x1, x2)), MARK(U51(isNatIListKind(z0), x1, x2))) A__U61(tt, U51(isNatKind(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatKind(z0), x1, x2)), MARK(U51(isNatKind(z0), x1, x2))) A__U61(tt, U51(cons(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(cons(mark(z0), z1), x1, x2)), MARK(U51(cons(z0, z1), x1, x2))) A__U61(tt, U51(0, x1, x2)) -> c26(A__LENGTH(a__U51(0, x1, x2)), MARK(U51(0, x1, x2))) A__U61(tt, U51(tt, x1, x2)) -> c26(A__LENGTH(a__U51(tt, x1, x2)), MARK(U51(tt, x1, x2))) A__U61(tt, U51(s(z0), x1, x2)) -> c26(A__LENGTH(a__U51(s(mark(z0)), x1, x2)), MARK(U51(s(z0), x1, x2))) A__U61(tt, U51(nil, x1, x2)) -> c26(A__LENGTH(a__U51(nil, x1, x2)), MARK(U51(nil, x1, 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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_1, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c14_2, c20_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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) 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MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> 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z2), x1, x2)), MARK(U51(U41(z0, z1, z2), x1, x2))) A__U61(tt, U51(U42(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U42(mark(z0), z1), x1, x2)), MARK(U51(U42(z0, z1), x1, x2))) A__U61(tt, U51(U43(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U43(mark(z0)), x1, x2)), MARK(U51(U43(z0), x1, x2))) A__U61(tt, U51(isNatIList(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatIList(z0), x1, x2)), MARK(U51(isNatIList(z0), x1, x2))) A__U61(tt, U51(U51(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U51(a__U51(mark(z0), z1, z2), x1, x2)), MARK(U51(U51(z0, z1, z2), x1, x2))) A__U61(tt, U51(U52(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U52(mark(z0), z1), x1, x2)), MARK(U51(U52(z0, z1), x1, x2))) A__U61(tt, U51(U53(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U53(mark(z0)), x1, x2)), MARK(U51(U53(z0), x1, x2))) A__U61(tt, U51(U61(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U61(mark(z0), z1), x1, x2)), MARK(U51(U61(z0, z1), x1, x2))) A__U61(tt, U51(length(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__length(mark(z0)), x1, x2)), MARK(U51(length(z0), x1, x2))) A__U61(tt, U51(and(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__and(mark(z0), z1), x1, x2)), MARK(U51(and(z0, z1), x1, x2))) A__U61(tt, U51(isNatIListKind(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatIListKind(z0), x1, x2)), MARK(U51(isNatIListKind(z0), x1, x2))) A__U61(tt, U51(isNatKind(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatKind(z0), x1, x2)), MARK(U51(isNatKind(z0), x1, x2))) A__U61(tt, U51(cons(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(cons(mark(z0), z1), x1, x2)), MARK(U51(cons(z0, z1), x1, x2))) A__U61(tt, U51(tt, x1, x2)) -> c26(A__LENGTH(a__U51(tt, x1, x2)), MARK(U51(tt, x1, x2))) A__U61(tt, U51(s(z0), x1, x2)) -> c26(A__LENGTH(a__U51(s(mark(z0)), x1, x2)), MARK(U51(s(z0), x1, x2))) A__U61(tt, U51(x0, z1, z2)) -> c26(MARK(U51(x0, z1, z2))) A__U61(tt, U51(0, x1, x2)) -> c26(A__LENGTH(a__U51(0, x1, x2))) A__U61(tt, U51(nil, x1, x2)) -> c26(A__LENGTH(a__U51(nil, x1, x2))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> 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MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, 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c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> c26(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U61(tt, U12(U21(z0, z1))) -> c26(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U61(tt, U12(U22(z0))) -> c26(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U61(tt, U12(isNat(z0))) -> c26(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U61(tt, U12(U31(z0, z1))) -> c26(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U61(tt, U12(U32(z0))) -> c26(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U61(tt, U12(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U61(tt, U12(U42(z0, z1))) -> c26(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U61(tt, U12(U43(z0))) -> c26(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U61(tt, U12(isNatIList(z0))) -> c26(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U61(tt, U12(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U61(tt, U12(U52(z0, z1))) -> c26(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U61(tt, U12(U53(z0))) -> c26(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U61(tt, U12(U61(z0, z1))) -> c26(A__LENGTH(a__U12(a__U61(mark(z0), z1))), MARK(U12(U61(z0, z1)))) A__U61(tt, U12(length(z0))) -> c26(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U61(tt, U12(and(z0, z1))) -> c26(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U61(tt, U12(isNatIListKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U61(tt, U12(isNatKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U61(tt, U12(cons(z0, z1))) -> c26(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U61(tt, U12(0)) -> c26(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U61(tt, U12(tt)) -> c26(A__LENGTH(a__U12(tt)), 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x1, x2))) A__U61(tt, U41(isNat(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNat(z0), x1, x2)), MARK(U41(isNat(z0), x1, x2))) A__U61(tt, U41(U31(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(U41(U31(z0, z1), x1, x2))) A__U61(tt, U41(U32(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U32(mark(z0)), x1, x2)), MARK(U41(U32(z0), x1, x2))) A__U61(tt, U41(U41(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2))) A__U61(tt, U41(U42(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U42(mark(z0), z1), x1, x2)), MARK(U41(U42(z0, z1), x1, x2))) A__U61(tt, U41(U43(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U43(mark(z0)), x1, x2)), MARK(U41(U43(z0), x1, x2))) A__U61(tt, U41(isNatIList(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatIList(z0), x1, x2)), MARK(U41(isNatIList(z0), x1, x2))) A__U61(tt, U41(U51(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U41(a__U51(mark(z0), z1, z2), x1, x2)), MARK(U41(U51(z0, z1, z2), x1, x2))) A__U61(tt, U41(U52(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U52(mark(z0), z1), x1, x2)), MARK(U41(U52(z0, z1), x1, x2))) A__U61(tt, U41(U53(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U53(mark(z0)), x1, x2)), MARK(U41(U53(z0), x1, x2))) A__U61(tt, U41(U61(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U61(mark(z0), z1), x1, x2)), MARK(U41(U61(z0, z1), x1, x2))) A__U61(tt, U41(length(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__length(mark(z0)), x1, x2)), MARK(U41(length(z0), x1, x2))) A__U61(tt, U41(and(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__and(mark(z0), z1), x1, x2)), MARK(U41(and(z0, z1), x1, x2))) A__U61(tt, U41(isNatIListKind(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatIListKind(z0), x1, x2)), MARK(U41(isNatIListKind(z0), x1, x2))) A__U61(tt, U41(isNatKind(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatKind(z0), x1, x2)), MARK(U41(isNatKind(z0), x1, x2))) A__U61(tt, U41(cons(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(cons(mark(z0), z1), x1, x2)), MARK(U41(cons(z0, z1), x1, x2))) A__U61(tt, U41(tt, x1, x2)) -> c26(A__LENGTH(a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2))) A__U61(tt, U41(s(z0), x1, x2)) -> c26(A__LENGTH(a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2))) A__U61(tt, U41(x0, z1, z2)) -> c26(MARK(U41(x0, z1, z2))) A__U61(tt, U41(0, x1, x2)) -> c26(A__LENGTH(a__U41(0, x1, x2))) A__U61(tt, U41(nil, x1, x2)) -> c26(A__LENGTH(a__U41(nil, x1, x2))) A__U61(tt, U42(zeros, x1)) -> c26(A__LENGTH(a__U42(a__zeros, x1)), MARK(U42(zeros, x1))) A__U61(tt, U42(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U11(mark(z0), z1), x1)), MARK(U42(U11(z0, z1), x1))) A__U61(tt, U42(U12(z0), x1)) -> c26(A__LENGTH(a__U42(a__U12(mark(z0)), x1)), MARK(U42(U12(z0), x1))) A__U61(tt, U42(isNatList(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatList(z0), x1)), MARK(U42(isNatList(z0), x1))) A__U61(tt, U42(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U21(mark(z0), z1), x1)), MARK(U42(U21(z0, z1), x1))) A__U61(tt, U42(U22(z0), x1)) -> c26(A__LENGTH(a__U42(a__U22(mark(z0)), x1)), MARK(U42(U22(z0), x1))) A__U61(tt, U42(isNat(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNat(z0), x1)), MARK(U42(isNat(z0), x1))) A__U61(tt, U42(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U31(mark(z0), z1), x1)), MARK(U42(U31(z0, z1), x1))) A__U61(tt, U42(U32(z0), x1)) -> c26(A__LENGTH(a__U42(a__U32(mark(z0)), x1)), MARK(U42(U32(z0), x1))) A__U61(tt, U42(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U42(a__U41(mark(z0), z1, z2), x1)), MARK(U42(U41(z0, z1, z2), x1))) A__U61(tt, U42(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U42(mark(z0), z1), x1)), MARK(U42(U42(z0, z1), x1))) A__U61(tt, U42(U43(z0), x1)) -> c26(A__LENGTH(a__U42(a__U43(mark(z0)), x1)), MARK(U42(U43(z0), x1))) A__U61(tt, U42(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatIList(z0), x1)), MARK(U42(isNatIList(z0), x1))) A__U61(tt, U42(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U42(a__U51(mark(z0), z1, z2), x1)), MARK(U42(U51(z0, z1, z2), x1))) A__U61(tt, U42(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U52(mark(z0), z1), x1)), MARK(U42(U52(z0, z1), x1))) A__U61(tt, U42(U53(z0), x1)) -> c26(A__LENGTH(a__U42(a__U53(mark(z0)), x1)), MARK(U42(U53(z0), x1))) A__U61(tt, U42(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U61(mark(z0), z1), x1)), MARK(U42(U61(z0, z1), x1))) A__U61(tt, U42(length(z0), x1)) -> c26(A__LENGTH(a__U42(a__length(mark(z0)), x1)), MARK(U42(length(z0), x1))) A__U61(tt, U42(and(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__and(mark(z0), z1), x1)), MARK(U42(and(z0, z1), x1))) A__U61(tt, U42(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatIListKind(z0), x1)), MARK(U42(isNatIListKind(z0), x1))) A__U61(tt, U42(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatKind(z0), x1)), MARK(U42(isNatKind(z0), x1))) A__U61(tt, U42(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U42(cons(mark(z0), z1), x1)), MARK(U42(cons(z0, z1), x1))) A__U61(tt, U42(tt, x1)) -> c26(A__LENGTH(a__U42(tt, x1)), MARK(U42(tt, x1))) A__U61(tt, U42(s(z0), x1)) -> c26(A__LENGTH(a__U42(s(mark(z0)), x1)), MARK(U42(s(z0), x1))) A__U61(tt, U42(x0, z1)) -> c26(MARK(U42(x0, z1))) A__U61(tt, U42(0, x1)) -> c26(A__LENGTH(a__U42(0, x1))) A__U61(tt, U42(nil, x1)) -> c26(A__LENGTH(a__U42(nil, x1))) A__U61(tt, U43(zeros)) -> c26(A__LENGTH(a__U43(a__zeros)), MARK(U43(zeros))) A__U61(tt, U43(U11(z0, z1))) -> c26(A__LENGTH(a__U43(a__U11(mark(z0), z1))), MARK(U43(U11(z0, z1)))) A__U61(tt, U43(U12(z0))) -> c26(A__LENGTH(a__U43(a__U12(mark(z0)))), MARK(U43(U12(z0)))) A__U61(tt, U43(isNatList(z0))) -> c26(A__LENGTH(a__U43(a__isNatList(z0))), MARK(U43(isNatList(z0)))) A__U61(tt, U43(U21(z0, z1))) -> c26(A__LENGTH(a__U43(a__U21(mark(z0), z1))), MARK(U43(U21(z0, z1)))) A__U61(tt, U43(U22(z0))) -> c26(A__LENGTH(a__U43(a__U22(mark(z0)))), MARK(U43(U22(z0)))) A__U61(tt, U43(isNat(z0))) -> c26(A__LENGTH(a__U43(a__isNat(z0))), MARK(U43(isNat(z0)))) A__U61(tt, U43(U31(z0, z1))) -> c26(A__LENGTH(a__U43(a__U31(mark(z0), z1))), MARK(U43(U31(z0, z1)))) A__U61(tt, U43(U32(z0))) -> c26(A__LENGTH(a__U43(a__U32(mark(z0)))), MARK(U43(U32(z0)))) A__U61(tt, U43(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U43(a__U41(mark(z0), z1, z2))), MARK(U43(U41(z0, z1, z2)))) A__U61(tt, U43(U42(z0, z1))) -> c26(A__LENGTH(a__U43(a__U42(mark(z0), z1))), MARK(U43(U42(z0, z1)))) A__U61(tt, U43(U43(z0))) -> c26(A__LENGTH(a__U43(a__U43(mark(z0)))), MARK(U43(U43(z0)))) A__U61(tt, U43(isNatIList(z0))) -> c26(A__LENGTH(a__U43(a__isNatIList(z0))), MARK(U43(isNatIList(z0)))) A__U61(tt, U43(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U43(a__U51(mark(z0), z1, z2))), MARK(U43(U51(z0, z1, z2)))) A__U61(tt, U43(U52(z0, z1))) -> c26(A__LENGTH(a__U43(a__U52(mark(z0), z1))), MARK(U43(U52(z0, z1)))) A__U61(tt, U43(U53(z0))) -> c26(A__LENGTH(a__U43(a__U53(mark(z0)))), MARK(U43(U53(z0)))) A__U61(tt, U43(U61(z0, z1))) -> c26(A__LENGTH(a__U43(a__U61(mark(z0), z1))), MARK(U43(U61(z0, z1)))) A__U61(tt, U43(length(z0))) -> c26(A__LENGTH(a__U43(a__length(mark(z0)))), MARK(U43(length(z0)))) A__U61(tt, U43(and(z0, z1))) -> c26(A__LENGTH(a__U43(a__and(mark(z0), z1))), MARK(U43(and(z0, z1)))) A__U61(tt, U43(isNatIListKind(z0))) -> c26(A__LENGTH(a__U43(a__isNatIListKind(z0))), MARK(U43(isNatIListKind(z0)))) A__U61(tt, U43(isNatKind(z0))) -> c26(A__LENGTH(a__U43(a__isNatKind(z0))), MARK(U43(isNatKind(z0)))) A__U61(tt, U43(cons(z0, z1))) -> c26(A__LENGTH(a__U43(cons(mark(z0), z1))), MARK(U43(cons(z0, z1)))) A__U61(tt, U43(0)) -> c26(A__LENGTH(a__U43(0)), MARK(U43(0))) A__U61(tt, U43(tt)) -> c26(A__LENGTH(a__U43(tt)), MARK(U43(tt))) A__U61(tt, U43(s(z0))) -> c26(A__LENGTH(a__U43(s(mark(z0)))), MARK(U43(s(z0)))) A__U61(tt, U43(nil)) -> c26(A__LENGTH(a__U43(nil)), MARK(U43(nil))) A__U61(tt, U43(x0)) -> c26(MARK(U43(x0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__U31(a__isNatIListKind(z0), z0)), MARK(isNatIList(z0))) A__U61(tt, isNatIList(cons(z0, z1))) -> c26(A__LENGTH(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatIList(cons(z0, z1)))) A__U61(tt, isNatIList(zeros)) -> c26(MARK(isNatIList(zeros))) A__U61(tt, isNatIList(z0)) -> c26(MARK(isNatIList(z0))) A__U61(tt, U51(zeros, x1, x2)) -> c26(A__LENGTH(a__U51(a__zeros, x1, x2)), MARK(U51(zeros, x1, x2))) A__U61(tt, U51(U11(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U11(mark(z0), z1), x1, x2)), MARK(U51(U11(z0, z1), x1, x2))) A__U61(tt, U51(U12(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U12(mark(z0)), x1, x2)), MARK(U51(U12(z0), x1, x2))) A__U61(tt, U51(isNatList(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatList(z0), x1, x2)), MARK(U51(isNatList(z0), x1, x2))) A__U61(tt, U51(U21(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U21(mark(z0), z1), x1, x2)), MARK(U51(U21(z0, z1), x1, x2))) A__U61(tt, U51(U22(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U22(mark(z0)), x1, x2)), MARK(U51(U22(z0), x1, x2))) A__U61(tt, U51(isNat(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNat(z0), x1, x2)), MARK(U51(isNat(z0), x1, x2))) A__U61(tt, U51(U31(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U31(mark(z0), z1), x1, x2)), MARK(U51(U31(z0, z1), x1, x2))) A__U61(tt, U51(U32(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U32(mark(z0)), x1, x2)), MARK(U51(U32(z0), x1, x2))) A__U61(tt, U51(U41(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U51(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U51(U41(z0, z1, z2), x1, x2))) A__U61(tt, U51(U42(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U42(mark(z0), z1), x1, x2)), MARK(U51(U42(z0, z1), x1, x2))) A__U61(tt, U51(U43(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U43(mark(z0)), x1, x2)), MARK(U51(U43(z0), x1, x2))) A__U61(tt, U51(isNatIList(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatIList(z0), x1, x2)), MARK(U51(isNatIList(z0), x1, x2))) A__U61(tt, U51(U51(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U51(a__U51(mark(z0), z1, z2), x1, x2)), MARK(U51(U51(z0, z1, z2), x1, x2))) A__U61(tt, U51(U52(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U52(mark(z0), z1), x1, x2)), MARK(U51(U52(z0, z1), x1, x2))) A__U61(tt, U51(U53(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U53(mark(z0)), x1, x2)), MARK(U51(U53(z0), x1, x2))) A__U61(tt, U51(U61(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U61(mark(z0), z1), x1, x2)), MARK(U51(U61(z0, z1), x1, x2))) A__U61(tt, U51(length(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__length(mark(z0)), x1, x2)), MARK(U51(length(z0), x1, x2))) A__U61(tt, U51(and(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__and(mark(z0), z1), x1, x2)), MARK(U51(and(z0, z1), x1, x2))) A__U61(tt, U51(isNatIListKind(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatIListKind(z0), x1, x2)), MARK(U51(isNatIListKind(z0), x1, x2))) A__U61(tt, U51(isNatKind(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatKind(z0), x1, x2)), MARK(U51(isNatKind(z0), x1, x2))) A__U61(tt, U51(cons(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(cons(mark(z0), z1), x1, x2)), MARK(U51(cons(z0, z1), x1, x2))) A__U61(tt, U51(tt, x1, x2)) -> c26(A__LENGTH(a__U51(tt, x1, x2)), MARK(U51(tt, x1, x2))) A__U61(tt, U51(s(z0), x1, x2)) -> c26(A__LENGTH(a__U51(s(mark(z0)), x1, x2)), MARK(U51(s(z0), x1, x2))) A__U61(tt, U51(x0, z1, z2)) -> c26(MARK(U51(x0, z1, z2))) A__U61(tt, U51(0, x1, x2)) -> c26(A__LENGTH(a__U51(0, x1, x2))) A__U61(tt, U51(nil, x1, x2)) -> c26(A__LENGTH(a__U51(nil, x1, 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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_1, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c14_2, c20_2 ---------------------------------------- (199) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U61(tt, U52(z0, z1)) -> c26(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) by A__U61(tt, U52(x0, z1)) -> c26(A__LENGTH(U52(mark(x0), z1)), MARK(U52(x0, z1))) A__U61(tt, U52(zeros, x1)) -> c26(A__LENGTH(a__U52(a__zeros, x1)), MARK(U52(zeros, x1))) A__U61(tt, U52(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U11(mark(z0), z1), x1)), MARK(U52(U11(z0, z1), x1))) A__U61(tt, U52(U12(z0), x1)) -> c26(A__LENGTH(a__U52(a__U12(mark(z0)), x1)), MARK(U52(U12(z0), x1))) A__U61(tt, U52(isNatList(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatList(z0), x1)), MARK(U52(isNatList(z0), x1))) A__U61(tt, U52(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U21(mark(z0), z1), x1)), MARK(U52(U21(z0, z1), x1))) A__U61(tt, U52(U22(z0), x1)) -> c26(A__LENGTH(a__U52(a__U22(mark(z0)), x1)), MARK(U52(U22(z0), x1))) A__U61(tt, U52(isNat(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNat(z0), x1)), MARK(U52(isNat(z0), x1))) A__U61(tt, U52(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U31(mark(z0), z1), x1)), MARK(U52(U31(z0, z1), x1))) A__U61(tt, U52(U32(z0), x1)) -> c26(A__LENGTH(a__U52(a__U32(mark(z0)), x1)), MARK(U52(U32(z0), x1))) A__U61(tt, U52(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U52(a__U41(mark(z0), z1, z2), x1)), MARK(U52(U41(z0, z1, z2), x1))) A__U61(tt, U52(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U42(mark(z0), z1), x1)), MARK(U52(U42(z0, z1), x1))) A__U61(tt, U52(U43(z0), x1)) -> c26(A__LENGTH(a__U52(a__U43(mark(z0)), x1)), MARK(U52(U43(z0), x1))) A__U61(tt, U52(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatIList(z0), x1)), MARK(U52(isNatIList(z0), x1))) A__U61(tt, U52(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U52(a__U51(mark(z0), z1, z2), x1)), MARK(U52(U51(z0, z1, z2), x1))) A__U61(tt, U52(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U52(mark(z0), z1), x1)), MARK(U52(U52(z0, z1), x1))) A__U61(tt, U52(U53(z0), x1)) -> c26(A__LENGTH(a__U52(a__U53(mark(z0)), x1)), MARK(U52(U53(z0), x1))) A__U61(tt, U52(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U61(mark(z0), z1), x1)), MARK(U52(U61(z0, z1), x1))) A__U61(tt, U52(length(z0), x1)) -> c26(A__LENGTH(a__U52(a__length(mark(z0)), x1)), MARK(U52(length(z0), x1))) A__U61(tt, U52(and(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__and(mark(z0), z1), x1)), MARK(U52(and(z0, z1), x1))) A__U61(tt, U52(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatIListKind(z0), x1)), MARK(U52(isNatIListKind(z0), x1))) A__U61(tt, U52(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatKind(z0), x1)), MARK(U52(isNatKind(z0), x1))) A__U61(tt, U52(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U52(cons(mark(z0), z1), x1)), MARK(U52(cons(z0, z1), x1))) A__U61(tt, U52(0, x1)) -> c26(A__LENGTH(a__U52(0, x1)), MARK(U52(0, x1))) A__U61(tt, U52(tt, x1)) -> c26(A__LENGTH(a__U52(tt, x1)), MARK(U52(tt, x1))) A__U61(tt, U52(s(z0), x1)) -> c26(A__LENGTH(a__U52(s(mark(z0)), x1)), MARK(U52(s(z0), x1))) A__U61(tt, U52(nil, x1)) -> c26(A__LENGTH(a__U52(nil, x1)), MARK(U52(nil, 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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), 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MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> c26(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U61(tt, U12(U21(z0, z1))) -> c26(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U61(tt, U12(U22(z0))) -> c26(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U61(tt, U12(isNat(z0))) -> c26(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U61(tt, U12(U31(z0, z1))) -> c26(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U61(tt, U12(U32(z0))) -> c26(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U61(tt, U12(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U61(tt, U12(U42(z0, z1))) -> c26(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U61(tt, U12(U43(z0))) -> c26(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U61(tt, U12(isNatIList(z0))) -> c26(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U61(tt, U12(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U61(tt, U12(U52(z0, z1))) -> c26(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U61(tt, U12(U53(z0))) -> c26(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U61(tt, U12(U61(z0, z1))) -> c26(A__LENGTH(a__U12(a__U61(mark(z0), z1))), MARK(U12(U61(z0, z1)))) A__U61(tt, U12(length(z0))) -> c26(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U61(tt, U12(and(z0, z1))) -> c26(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U61(tt, U12(isNatIListKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U61(tt, U12(isNatKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U61(tt, U12(cons(z0, z1))) -> c26(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U61(tt, U12(0)) -> c26(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U61(tt, U12(tt)) -> c26(A__LENGTH(a__U12(tt)), MARK(U12(tt))) A__U61(tt, U12(s(z0))) -> c26(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U61(tt, U12(nil)) -> c26(A__LENGTH(a__U12(nil)), MARK(U12(nil))) A__U61(tt, U12(x0)) -> c26(MARK(U12(x0))) A__U61(tt, isNatList(cons(z0, z1))) -> c26(A__LENGTH(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(cons(z0, z1)))) A__U61(tt, isNatList(nil)) -> c26(MARK(isNatList(nil))) A__U61(tt, isNatList(z0)) -> c26(MARK(isNatList(z0))) A__U61(tt, U21(zeros, x1)) -> c26(A__LENGTH(a__U21(a__zeros, x1)), MARK(U21(zeros, x1))) A__U61(tt, U21(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1)), MARK(U21(U11(z0, z1), x1))) A__U61(tt, U21(U12(z0), x1)) -> c26(A__LENGTH(a__U21(a__U12(mark(z0)), x1)), MARK(U21(U12(z0), x1))) A__U61(tt, U21(isNatList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatList(z0), x1)), MARK(U21(isNatList(z0), x1))) A__U61(tt, U21(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U21(mark(z0), z1), x1)), MARK(U21(U21(z0, z1), x1))) A__U61(tt, U21(U22(z0), x1)) -> c26(A__LENGTH(a__U21(a__U22(mark(z0)), x1)), MARK(U21(U22(z0), x1))) A__U61(tt, U21(isNat(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNat(z0), x1)), MARK(U21(isNat(z0), x1))) A__U61(tt, U21(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U31(mark(z0), z1), x1)), MARK(U21(U31(z0, z1), x1))) A__U61(tt, U21(U32(z0), x1)) -> c26(A__LENGTH(a__U21(a__U32(mark(z0)), x1)), MARK(U21(U32(z0), x1))) A__U61(tt, U21(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(U21(U41(z0, z1, z2), x1))) A__U61(tt, U21(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U42(mark(z0), z1), x1)), MARK(U21(U42(z0, z1), x1))) A__U61(tt, U21(U43(z0), x1)) -> c26(A__LENGTH(a__U21(a__U43(mark(z0)), x1)), MARK(U21(U43(z0), x1))) A__U61(tt, U21(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIList(z0), x1)), MARK(U21(isNatIList(z0), x1))) A__U61(tt, U21(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U51(mark(z0), z1, z2), x1)), MARK(U21(U51(z0, z1, z2), x1))) A__U61(tt, U21(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U52(mark(z0), z1), x1)), MARK(U21(U52(z0, z1), x1))) A__U61(tt, U21(U53(z0), x1)) -> c26(A__LENGTH(a__U21(a__U53(mark(z0)), x1)), MARK(U21(U53(z0), x1))) A__U61(tt, U21(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U61(mark(z0), z1), x1)), MARK(U21(U61(z0, z1), x1))) A__U61(tt, U21(length(z0), x1)) -> c26(A__LENGTH(a__U21(a__length(mark(z0)), x1)), MARK(U21(length(z0), x1))) A__U61(tt, U21(and(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__and(mark(z0), z1), x1)), MARK(U21(and(z0, z1), x1))) A__U61(tt, U21(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIListKind(z0), x1)), MARK(U21(isNatIListKind(z0), x1))) A__U61(tt, U21(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), x1)), MARK(U21(isNatKind(z0), x1))) A__U61(tt, U21(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U21(cons(mark(z0), z1), x1)), MARK(U21(cons(z0, z1), x1))) A__U61(tt, U21(tt, x1)) -> c26(A__LENGTH(a__U21(tt, x1)), MARK(U21(tt, x1))) A__U61(tt, U21(s(z0), x1)) -> c26(A__LENGTH(a__U21(s(mark(z0)), x1)), MARK(U21(s(z0), x1))) A__U61(tt, U21(x0, z1)) -> c26(MARK(U21(x0, z1))) A__U61(tt, U21(0, x1)) -> c26(A__LENGTH(a__U21(0, x1))) A__U61(tt, U21(nil, x1)) -> c26(A__LENGTH(a__U21(nil, x1))) A__U61(tt, U22(zeros)) -> c26(A__LENGTH(a__U22(a__zeros)), MARK(U22(zeros))) A__U61(tt, U22(U11(z0, z1))) -> c26(A__LENGTH(a__U22(a__U11(mark(z0), z1))), MARK(U22(U11(z0, z1)))) A__U61(tt, U22(U12(z0))) -> c26(A__LENGTH(a__U22(a__U12(mark(z0)))), MARK(U22(U12(z0)))) A__U61(tt, U22(isNatList(z0))) -> c26(A__LENGTH(a__U22(a__isNatList(z0))), MARK(U22(isNatList(z0)))) A__U61(tt, U22(U21(z0, z1))) -> c26(A__LENGTH(a__U22(a__U21(mark(z0), z1))), MARK(U22(U21(z0, z1)))) A__U61(tt, U22(U22(z0))) -> c26(A__LENGTH(a__U22(a__U22(mark(z0)))), MARK(U22(U22(z0)))) A__U61(tt, U22(isNat(z0))) -> c26(A__LENGTH(a__U22(a__isNat(z0))), MARK(U22(isNat(z0)))) A__U61(tt, U22(U31(z0, z1))) -> c26(A__LENGTH(a__U22(a__U31(mark(z0), z1))), MARK(U22(U31(z0, z1)))) A__U61(tt, U22(U32(z0))) -> c26(A__LENGTH(a__U22(a__U32(mark(z0)))), MARK(U22(U32(z0)))) A__U61(tt, U22(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U22(a__U41(mark(z0), z1, z2))), MARK(U22(U41(z0, z1, z2)))) A__U61(tt, U22(U42(z0, z1))) -> c26(A__LENGTH(a__U22(a__U42(mark(z0), z1))), MARK(U22(U42(z0, z1)))) A__U61(tt, U22(U43(z0))) -> c26(A__LENGTH(a__U22(a__U43(mark(z0)))), MARK(U22(U43(z0)))) A__U61(tt, U22(isNatIList(z0))) -> c26(A__LENGTH(a__U22(a__isNatIList(z0))), MARK(U22(isNatIList(z0)))) A__U61(tt, U22(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U22(a__U51(mark(z0), z1, z2))), MARK(U22(U51(z0, z1, z2)))) A__U61(tt, U22(U52(z0, z1))) -> c26(A__LENGTH(a__U22(a__U52(mark(z0), z1))), MARK(U22(U52(z0, z1)))) A__U61(tt, U22(U53(z0))) -> c26(A__LENGTH(a__U22(a__U53(mark(z0)))), MARK(U22(U53(z0)))) A__U61(tt, U22(U61(z0, z1))) -> c26(A__LENGTH(a__U22(a__U61(mark(z0), z1))), MARK(U22(U61(z0, z1)))) A__U61(tt, U22(length(z0))) -> c26(A__LENGTH(a__U22(a__length(mark(z0)))), MARK(U22(length(z0)))) A__U61(tt, U22(and(z0, z1))) -> c26(A__LENGTH(a__U22(a__and(mark(z0), z1))), MARK(U22(and(z0, z1)))) A__U61(tt, U22(isNatIListKind(z0))) -> c26(A__LENGTH(a__U22(a__isNatIListKind(z0))), MARK(U22(isNatIListKind(z0)))) A__U61(tt, U22(isNatKind(z0))) -> c26(A__LENGTH(a__U22(a__isNatKind(z0))), MARK(U22(isNatKind(z0)))) A__U61(tt, U22(cons(z0, z1))) -> c26(A__LENGTH(a__U22(cons(mark(z0), z1))), MARK(U22(cons(z0, z1)))) A__U61(tt, U22(0)) -> c26(A__LENGTH(a__U22(0)), MARK(U22(0))) A__U61(tt, U22(tt)) -> c26(A__LENGTH(a__U22(tt)), MARK(U22(tt))) A__U61(tt, U22(s(z0))) -> c26(A__LENGTH(a__U22(s(mark(z0)))), MARK(U22(s(z0)))) A__U61(tt, U22(nil)) -> c26(A__LENGTH(a__U22(nil)), MARK(U22(nil))) A__U61(tt, U22(x0)) -> c26(MARK(U22(x0))) A__U61(tt, isNat(length(z0))) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), z0)), MARK(isNat(length(z0)))) A__U61(tt, isNat(s(z0))) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), z0)), MARK(isNat(s(z0)))) A__U61(tt, isNat(0)) -> c26(MARK(isNat(0))) A__U61(tt, isNat(z0)) -> c26(MARK(isNat(z0))) A__U61(tt, U31(zeros, x1)) -> c26(A__LENGTH(a__U31(a__zeros, x1)), MARK(U31(zeros, x1))) A__U61(tt, U31(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U11(mark(z0), z1), x1)), MARK(U31(U11(z0, z1), x1))) A__U61(tt, U31(U12(z0), x1)) -> c26(A__LENGTH(a__U31(a__U12(mark(z0)), x1)), MARK(U31(U12(z0), x1))) A__U61(tt, U31(isNatList(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatList(z0), x1)), MARK(U31(isNatList(z0), x1))) A__U61(tt, U31(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U21(mark(z0), z1), x1)), MARK(U31(U21(z0, z1), x1))) A__U61(tt, U31(U22(z0), x1)) -> c26(A__LENGTH(a__U31(a__U22(mark(z0)), x1)), MARK(U31(U22(z0), x1))) A__U61(tt, U31(isNat(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNat(z0), x1)), MARK(U31(isNat(z0), x1))) A__U61(tt, U31(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U31(mark(z0), z1), x1)), MARK(U31(U31(z0, z1), x1))) A__U61(tt, U31(U32(z0), x1)) -> c26(A__LENGTH(a__U31(a__U32(mark(z0)), x1)), MARK(U31(U32(z0), x1))) A__U61(tt, U31(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(U31(U41(z0, z1, z2), x1))) A__U61(tt, U31(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U42(mark(z0), z1), x1)), MARK(U31(U42(z0, z1), x1))) A__U61(tt, U31(U43(z0), x1)) -> c26(A__LENGTH(a__U31(a__U43(mark(z0)), x1)), MARK(U31(U43(z0), x1))) A__U61(tt, U31(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatIList(z0), x1)), MARK(U31(isNatIList(z0), x1))) A__U61(tt, U31(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U31(a__U51(mark(z0), z1, z2), x1)), MARK(U31(U51(z0, z1, z2), x1))) A__U61(tt, U31(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U52(mark(z0), z1), x1)), MARK(U31(U52(z0, z1), x1))) A__U61(tt, U31(U53(z0), x1)) -> c26(A__LENGTH(a__U31(a__U53(mark(z0)), x1)), MARK(U31(U53(z0), x1))) A__U61(tt, U31(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U61(mark(z0), z1), x1)), MARK(U31(U61(z0, z1), x1))) A__U61(tt, U31(length(z0), x1)) -> c26(A__LENGTH(a__U31(a__length(mark(z0)), x1)), MARK(U31(length(z0), x1))) A__U61(tt, U31(and(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__and(mark(z0), z1), x1)), MARK(U31(and(z0, z1), x1))) A__U61(tt, U31(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatIListKind(z0), x1)), MARK(U31(isNatIListKind(z0), x1))) A__U61(tt, U31(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatKind(z0), x1)), MARK(U31(isNatKind(z0), x1))) A__U61(tt, U31(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U31(cons(mark(z0), z1), x1)), MARK(U31(cons(z0, z1), x1))) A__U61(tt, U31(tt, x1)) -> c26(A__LENGTH(a__U31(tt, x1)), MARK(U31(tt, x1))) A__U61(tt, U31(s(z0), x1)) -> c26(A__LENGTH(a__U31(s(mark(z0)), x1)), MARK(U31(s(z0), x1))) A__U61(tt, U31(x0, z1)) -> c26(MARK(U31(x0, z1))) A__U61(tt, U31(0, x1)) -> c26(A__LENGTH(a__U31(0, x1))) A__U61(tt, U31(nil, x1)) -> c26(A__LENGTH(a__U31(nil, x1))) A__U61(tt, U32(zeros)) -> c26(A__LENGTH(a__U32(a__zeros)), MARK(U32(zeros))) A__U61(tt, U32(U11(z0, z1))) -> c26(A__LENGTH(a__U32(a__U11(mark(z0), z1))), MARK(U32(U11(z0, z1)))) A__U61(tt, U32(U12(z0))) -> c26(A__LENGTH(a__U32(a__U12(mark(z0)))), MARK(U32(U12(z0)))) A__U61(tt, U32(isNatList(z0))) -> c26(A__LENGTH(a__U32(a__isNatList(z0))), MARK(U32(isNatList(z0)))) A__U61(tt, U32(U21(z0, z1))) -> c26(A__LENGTH(a__U32(a__U21(mark(z0), z1))), MARK(U32(U21(z0, z1)))) A__U61(tt, U32(U22(z0))) -> c26(A__LENGTH(a__U32(a__U22(mark(z0)))), MARK(U32(U22(z0)))) A__U61(tt, U32(isNat(z0))) -> c26(A__LENGTH(a__U32(a__isNat(z0))), MARK(U32(isNat(z0)))) A__U61(tt, U32(U31(z0, z1))) -> c26(A__LENGTH(a__U32(a__U31(mark(z0), z1))), MARK(U32(U31(z0, z1)))) A__U61(tt, U32(U32(z0))) -> c26(A__LENGTH(a__U32(a__U32(mark(z0)))), MARK(U32(U32(z0)))) A__U61(tt, U32(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U32(a__U41(mark(z0), z1, z2))), MARK(U32(U41(z0, z1, z2)))) A__U61(tt, U32(U42(z0, z1))) -> c26(A__LENGTH(a__U32(a__U42(mark(z0), z1))), MARK(U32(U42(z0, z1)))) A__U61(tt, U32(U43(z0))) -> c26(A__LENGTH(a__U32(a__U43(mark(z0)))), MARK(U32(U43(z0)))) A__U61(tt, U32(isNatIList(z0))) -> c26(A__LENGTH(a__U32(a__isNatIList(z0))), MARK(U32(isNatIList(z0)))) A__U61(tt, U32(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U32(a__U51(mark(z0), z1, z2))), MARK(U32(U51(z0, z1, z2)))) A__U61(tt, U32(U52(z0, z1))) -> c26(A__LENGTH(a__U32(a__U52(mark(z0), z1))), MARK(U32(U52(z0, z1)))) A__U61(tt, U32(U53(z0))) -> c26(A__LENGTH(a__U32(a__U53(mark(z0)))), MARK(U32(U53(z0)))) A__U61(tt, U32(U61(z0, z1))) -> c26(A__LENGTH(a__U32(a__U61(mark(z0), z1))), MARK(U32(U61(z0, z1)))) A__U61(tt, U32(length(z0))) -> c26(A__LENGTH(a__U32(a__length(mark(z0)))), MARK(U32(length(z0)))) A__U61(tt, U32(and(z0, z1))) -> c26(A__LENGTH(a__U32(a__and(mark(z0), z1))), MARK(U32(and(z0, z1)))) A__U61(tt, U32(isNatIListKind(z0))) -> c26(A__LENGTH(a__U32(a__isNatIListKind(z0))), MARK(U32(isNatIListKind(z0)))) A__U61(tt, U32(isNatKind(z0))) -> c26(A__LENGTH(a__U32(a__isNatKind(z0))), MARK(U32(isNatKind(z0)))) A__U61(tt, U32(cons(z0, z1))) -> c26(A__LENGTH(a__U32(cons(mark(z0), z1))), MARK(U32(cons(z0, z1)))) A__U61(tt, 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z2))) A__U61(tt, U51(0, x1, x2)) -> c26(A__LENGTH(a__U51(0, x1, x2))) A__U61(tt, U51(nil, x1, x2)) -> c26(A__LENGTH(a__U51(nil, x1, x2))) A__U61(tt, U52(x0, z1)) -> c26(A__LENGTH(U52(mark(x0), z1)), MARK(U52(x0, z1))) A__U61(tt, U52(zeros, x1)) -> c26(A__LENGTH(a__U52(a__zeros, x1)), MARK(U52(zeros, x1))) A__U61(tt, U52(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U11(mark(z0), z1), x1)), MARK(U52(U11(z0, z1), x1))) A__U61(tt, U52(U12(z0), x1)) -> c26(A__LENGTH(a__U52(a__U12(mark(z0)), x1)), MARK(U52(U12(z0), x1))) A__U61(tt, U52(isNatList(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatList(z0), x1)), MARK(U52(isNatList(z0), x1))) A__U61(tt, U52(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U21(mark(z0), z1), x1)), MARK(U52(U21(z0, z1), x1))) A__U61(tt, U52(U22(z0), x1)) -> c26(A__LENGTH(a__U52(a__U22(mark(z0)), x1)), MARK(U52(U22(z0), x1))) A__U61(tt, U52(isNat(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNat(z0), x1)), MARK(U52(isNat(z0), x1))) A__U61(tt, U52(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U31(mark(z0), z1), x1)), MARK(U52(U31(z0, z1), x1))) A__U61(tt, U52(U32(z0), x1)) -> c26(A__LENGTH(a__U52(a__U32(mark(z0)), x1)), MARK(U52(U32(z0), x1))) A__U61(tt, U52(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U52(a__U41(mark(z0), z1, z2), x1)), MARK(U52(U41(z0, z1, z2), x1))) A__U61(tt, U52(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U42(mark(z0), z1), x1)), MARK(U52(U42(z0, z1), x1))) A__U61(tt, U52(U43(z0), x1)) -> c26(A__LENGTH(a__U52(a__U43(mark(z0)), x1)), MARK(U52(U43(z0), x1))) A__U61(tt, U52(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatIList(z0), x1)), MARK(U52(isNatIList(z0), x1))) A__U61(tt, U52(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U52(a__U51(mark(z0), z1, z2), x1)), MARK(U52(U51(z0, z1, z2), x1))) A__U61(tt, U52(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U52(mark(z0), z1), x1)), MARK(U52(U52(z0, z1), x1))) A__U61(tt, U52(U53(z0), x1)) -> c26(A__LENGTH(a__U52(a__U53(mark(z0)), x1)), MARK(U52(U53(z0), x1))) A__U61(tt, U52(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U61(mark(z0), z1), x1)), MARK(U52(U61(z0, z1), x1))) A__U61(tt, U52(length(z0), x1)) -> c26(A__LENGTH(a__U52(a__length(mark(z0)), x1)), MARK(U52(length(z0), x1))) A__U61(tt, U52(and(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__and(mark(z0), z1), x1)), MARK(U52(and(z0, z1), x1))) A__U61(tt, U52(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatIListKind(z0), x1)), MARK(U52(isNatIListKind(z0), x1))) A__U61(tt, U52(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatKind(z0), x1)), MARK(U52(isNatKind(z0), x1))) A__U61(tt, U52(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U52(cons(mark(z0), z1), x1)), MARK(U52(cons(z0, z1), x1))) A__U61(tt, U52(0, x1)) -> c26(A__LENGTH(a__U52(0, x1)), MARK(U52(0, x1))) A__U61(tt, U52(tt, x1)) -> c26(A__LENGTH(a__U52(tt, x1)), MARK(U52(tt, x1))) A__U61(tt, U52(s(z0), x1)) -> c26(A__LENGTH(a__U52(s(mark(z0)), x1)), MARK(U52(s(z0), x1))) A__U61(tt, U52(nil, x1)) -> c26(A__LENGTH(a__U52(nil, x1)), MARK(U52(nil, x1))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, 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MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> c26(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U61(tt, U12(U21(z0, z1))) -> c26(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U61(tt, U12(U22(z0))) -> c26(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U61(tt, U12(isNat(z0))) -> c26(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U61(tt, U12(U31(z0, z1))) -> c26(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U61(tt, U12(U32(z0))) -> c26(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U61(tt, U12(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U61(tt, U12(U42(z0, z1))) -> c26(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U61(tt, U12(U43(z0))) -> c26(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U61(tt, U12(isNatIList(z0))) -> c26(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U61(tt, U12(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U61(tt, U12(U52(z0, z1))) -> c26(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U61(tt, U12(U53(z0))) -> c26(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U61(tt, U12(U61(z0, z1))) -> c26(A__LENGTH(a__U12(a__U61(mark(z0), z1))), MARK(U12(U61(z0, z1)))) A__U61(tt, U12(length(z0))) -> c26(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U61(tt, U12(and(z0, z1))) -> c26(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U61(tt, U12(isNatIListKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U61(tt, U12(isNatKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U61(tt, U12(cons(z0, z1))) -> c26(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U61(tt, U12(0)) -> c26(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U61(tt, U12(tt)) -> c26(A__LENGTH(a__U12(tt)), MARK(U12(tt))) A__U61(tt, U12(s(z0))) -> c26(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U61(tt, U12(nil)) -> c26(A__LENGTH(a__U12(nil)), MARK(U12(nil))) A__U61(tt, U12(x0)) -> c26(MARK(U12(x0))) A__U61(tt, isNatList(cons(z0, z1))) -> c26(A__LENGTH(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(cons(z0, z1)))) A__U61(tt, isNatList(nil)) -> c26(MARK(isNatList(nil))) A__U61(tt, isNatList(z0)) -> c26(MARK(isNatList(z0))) A__U61(tt, U21(zeros, x1)) -> c26(A__LENGTH(a__U21(a__zeros, x1)), MARK(U21(zeros, x1))) A__U61(tt, U21(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1)), MARK(U21(U11(z0, z1), x1))) A__U61(tt, U21(U12(z0), x1)) -> c26(A__LENGTH(a__U21(a__U12(mark(z0)), x1)), MARK(U21(U12(z0), x1))) A__U61(tt, U21(isNatList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatList(z0), x1)), MARK(U21(isNatList(z0), x1))) A__U61(tt, U21(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U21(mark(z0), z1), x1)), MARK(U21(U21(z0, z1), x1))) 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A__U61(tt, U21(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U52(mark(z0), z1), x1)), MARK(U21(U52(z0, z1), x1))) A__U61(tt, U21(U53(z0), x1)) -> c26(A__LENGTH(a__U21(a__U53(mark(z0)), x1)), MARK(U21(U53(z0), x1))) A__U61(tt, U21(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U61(mark(z0), z1), x1)), MARK(U21(U61(z0, z1), x1))) A__U61(tt, U21(length(z0), x1)) -> c26(A__LENGTH(a__U21(a__length(mark(z0)), x1)), MARK(U21(length(z0), x1))) A__U61(tt, U21(and(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__and(mark(z0), z1), x1)), MARK(U21(and(z0, z1), x1))) A__U61(tt, U21(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIListKind(z0), x1)), MARK(U21(isNatIListKind(z0), x1))) A__U61(tt, U21(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), x1)), MARK(U21(isNatKind(z0), x1))) A__U61(tt, U21(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U21(cons(mark(z0), z1), x1)), MARK(U21(cons(z0, z1), x1))) A__U61(tt, U21(tt, x1)) -> c26(A__LENGTH(a__U21(tt, x1)), MARK(U21(tt, x1))) A__U61(tt, 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A__U61(tt, U41(U52(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U52(mark(z0), z1), x1, x2)), MARK(U41(U52(z0, z1), x1, x2))) A__U61(tt, U41(U53(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U53(mark(z0)), x1, x2)), MARK(U41(U53(z0), x1, x2))) A__U61(tt, U41(U61(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U61(mark(z0), z1), x1, x2)), MARK(U41(U61(z0, z1), x1, x2))) A__U61(tt, U41(length(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__length(mark(z0)), x1, x2)), MARK(U41(length(z0), x1, x2))) A__U61(tt, U41(and(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__and(mark(z0), z1), x1, x2)), MARK(U41(and(z0, z1), x1, x2))) A__U61(tt, U41(isNatIListKind(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatIListKind(z0), x1, x2)), MARK(U41(isNatIListKind(z0), x1, x2))) A__U61(tt, U41(isNatKind(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatKind(z0), x1, x2)), MARK(U41(isNatKind(z0), x1, x2))) A__U61(tt, U41(cons(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(cons(mark(z0), z1), x1, x2)), MARK(U41(cons(z0, z1), x1, x2))) A__U61(tt, U41(tt, x1, x2)) -> c26(A__LENGTH(a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2))) A__U61(tt, U41(s(z0), x1, x2)) -> c26(A__LENGTH(a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2))) A__U61(tt, U41(x0, z1, z2)) -> c26(MARK(U41(x0, z1, z2))) A__U61(tt, U41(0, x1, x2)) -> c26(A__LENGTH(a__U41(0, x1, x2))) A__U61(tt, U41(nil, x1, x2)) -> c26(A__LENGTH(a__U41(nil, x1, x2))) A__U61(tt, U42(zeros, x1)) -> c26(A__LENGTH(a__U42(a__zeros, x1)), MARK(U42(zeros, x1))) A__U61(tt, U42(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U11(mark(z0), z1), x1)), MARK(U42(U11(z0, z1), x1))) A__U61(tt, U42(U12(z0), x1)) -> c26(A__LENGTH(a__U42(a__U12(mark(z0)), x1)), MARK(U42(U12(z0), x1))) A__U61(tt, U42(isNatList(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatList(z0), x1)), MARK(U42(isNatList(z0), x1))) A__U61(tt, U42(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U21(mark(z0), z1), x1)), MARK(U42(U21(z0, z1), x1))) A__U61(tt, U42(U22(z0), x1)) -> c26(A__LENGTH(a__U42(a__U22(mark(z0)), x1)), MARK(U42(U22(z0), x1))) A__U61(tt, U42(isNat(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNat(z0), x1)), MARK(U42(isNat(z0), x1))) A__U61(tt, U42(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U31(mark(z0), z1), x1)), MARK(U42(U31(z0, z1), x1))) A__U61(tt, U42(U32(z0), x1)) -> c26(A__LENGTH(a__U42(a__U32(mark(z0)), x1)), MARK(U42(U32(z0), x1))) A__U61(tt, U42(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U42(a__U41(mark(z0), z1, z2), x1)), MARK(U42(U41(z0, z1, z2), x1))) A__U61(tt, U42(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U42(mark(z0), z1), x1)), MARK(U42(U42(z0, z1), x1))) A__U61(tt, U42(U43(z0), x1)) -> c26(A__LENGTH(a__U42(a__U43(mark(z0)), x1)), MARK(U42(U43(z0), x1))) A__U61(tt, U42(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatIList(z0), x1)), MARK(U42(isNatIList(z0), x1))) A__U61(tt, U42(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U42(a__U51(mark(z0), z1, z2), x1)), MARK(U42(U51(z0, z1, z2), x1))) A__U61(tt, U42(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U52(mark(z0), z1), x1)), MARK(U42(U52(z0, z1), x1))) A__U61(tt, U42(U53(z0), x1)) -> c26(A__LENGTH(a__U42(a__U53(mark(z0)), x1)), MARK(U42(U53(z0), x1))) A__U61(tt, U42(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U61(mark(z0), z1), x1)), MARK(U42(U61(z0, z1), x1))) A__U61(tt, U42(length(z0), x1)) -> c26(A__LENGTH(a__U42(a__length(mark(z0)), x1)), MARK(U42(length(z0), x1))) A__U61(tt, U42(and(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__and(mark(z0), z1), x1)), MARK(U42(and(z0, z1), x1))) A__U61(tt, U42(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatIListKind(z0), x1)), MARK(U42(isNatIListKind(z0), x1))) A__U61(tt, U42(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatKind(z0), x1)), MARK(U42(isNatKind(z0), x1))) A__U61(tt, U42(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U42(cons(mark(z0), z1), x1)), MARK(U42(cons(z0, z1), x1))) A__U61(tt, U42(tt, x1)) -> c26(A__LENGTH(a__U42(tt, x1)), MARK(U42(tt, x1))) A__U61(tt, U42(s(z0), x1)) -> c26(A__LENGTH(a__U42(s(mark(z0)), x1)), MARK(U42(s(z0), x1))) A__U61(tt, U42(x0, z1)) -> c26(MARK(U42(x0, z1))) A__U61(tt, U42(0, x1)) -> c26(A__LENGTH(a__U42(0, x1))) A__U61(tt, U42(nil, x1)) -> c26(A__LENGTH(a__U42(nil, x1))) A__U61(tt, U43(zeros)) -> c26(A__LENGTH(a__U43(a__zeros)), MARK(U43(zeros))) A__U61(tt, U43(U11(z0, z1))) -> c26(A__LENGTH(a__U43(a__U11(mark(z0), z1))), MARK(U43(U11(z0, z1)))) A__U61(tt, U43(U12(z0))) -> c26(A__LENGTH(a__U43(a__U12(mark(z0)))), MARK(U43(U12(z0)))) A__U61(tt, U43(isNatList(z0))) -> c26(A__LENGTH(a__U43(a__isNatList(z0))), MARK(U43(isNatList(z0)))) A__U61(tt, U43(U21(z0, z1))) -> c26(A__LENGTH(a__U43(a__U21(mark(z0), z1))), MARK(U43(U21(z0, z1)))) A__U61(tt, U43(U22(z0))) -> c26(A__LENGTH(a__U43(a__U22(mark(z0)))), MARK(U43(U22(z0)))) A__U61(tt, U43(isNat(z0))) -> c26(A__LENGTH(a__U43(a__isNat(z0))), MARK(U43(isNat(z0)))) A__U61(tt, U43(U31(z0, z1))) -> c26(A__LENGTH(a__U43(a__U31(mark(z0), z1))), MARK(U43(U31(z0, z1)))) A__U61(tt, U43(U32(z0))) -> c26(A__LENGTH(a__U43(a__U32(mark(z0)))), MARK(U43(U32(z0)))) A__U61(tt, U43(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U43(a__U41(mark(z0), z1, z2))), MARK(U43(U41(z0, z1, z2)))) A__U61(tt, U43(U42(z0, z1))) -> c26(A__LENGTH(a__U43(a__U42(mark(z0), z1))), MARK(U43(U42(z0, z1)))) A__U61(tt, U43(U43(z0))) -> c26(A__LENGTH(a__U43(a__U43(mark(z0)))), MARK(U43(U43(z0)))) A__U61(tt, U43(isNatIList(z0))) -> c26(A__LENGTH(a__U43(a__isNatIList(z0))), MARK(U43(isNatIList(z0)))) A__U61(tt, U43(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U43(a__U51(mark(z0), z1, z2))), MARK(U43(U51(z0, z1, z2)))) A__U61(tt, U43(U52(z0, z1))) -> c26(A__LENGTH(a__U43(a__U52(mark(z0), z1))), MARK(U43(U52(z0, z1)))) A__U61(tt, U43(U53(z0))) -> c26(A__LENGTH(a__U43(a__U53(mark(z0)))), MARK(U43(U53(z0)))) A__U61(tt, U43(U61(z0, z1))) -> c26(A__LENGTH(a__U43(a__U61(mark(z0), z1))), MARK(U43(U61(z0, z1)))) A__U61(tt, U43(length(z0))) -> c26(A__LENGTH(a__U43(a__length(mark(z0)))), MARK(U43(length(z0)))) A__U61(tt, U43(and(z0, z1))) -> c26(A__LENGTH(a__U43(a__and(mark(z0), z1))), MARK(U43(and(z0, z1)))) A__U61(tt, U43(isNatIListKind(z0))) -> c26(A__LENGTH(a__U43(a__isNatIListKind(z0))), MARK(U43(isNatIListKind(z0)))) A__U61(tt, U43(isNatKind(z0))) -> c26(A__LENGTH(a__U43(a__isNatKind(z0))), MARK(U43(isNatKind(z0)))) A__U61(tt, U43(cons(z0, z1))) -> c26(A__LENGTH(a__U43(cons(mark(z0), z1))), MARK(U43(cons(z0, z1)))) A__U61(tt, U43(0)) -> c26(A__LENGTH(a__U43(0)), MARK(U43(0))) A__U61(tt, U43(tt)) -> c26(A__LENGTH(a__U43(tt)), MARK(U43(tt))) A__U61(tt, U43(s(z0))) -> c26(A__LENGTH(a__U43(s(mark(z0)))), MARK(U43(s(z0)))) A__U61(tt, U43(nil)) -> c26(A__LENGTH(a__U43(nil)), MARK(U43(nil))) A__U61(tt, U43(x0)) -> c26(MARK(U43(x0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__U31(a__isNatIListKind(z0), z0)), MARK(isNatIList(z0))) A__U61(tt, isNatIList(cons(z0, z1))) -> c26(A__LENGTH(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatIList(cons(z0, z1)))) A__U61(tt, isNatIList(zeros)) -> c26(MARK(isNatIList(zeros))) A__U61(tt, isNatIList(z0)) -> c26(MARK(isNatIList(z0))) A__U61(tt, U51(zeros, x1, x2)) -> c26(A__LENGTH(a__U51(a__zeros, x1, x2)), MARK(U51(zeros, x1, x2))) A__U61(tt, U51(U11(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U11(mark(z0), z1), x1, x2)), MARK(U51(U11(z0, z1), x1, x2))) A__U61(tt, U51(U12(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U12(mark(z0)), x1, x2)), MARK(U51(U12(z0), x1, x2))) A__U61(tt, U51(isNatList(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatList(z0), x1, x2)), MARK(U51(isNatList(z0), x1, x2))) A__U61(tt, U51(U21(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U21(mark(z0), z1), x1, x2)), MARK(U51(U21(z0, z1), x1, x2))) A__U61(tt, U51(U22(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U22(mark(z0)), x1, x2)), MARK(U51(U22(z0), x1, x2))) A__U61(tt, U51(isNat(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNat(z0), x1, x2)), MARK(U51(isNat(z0), x1, x2))) A__U61(tt, U51(U31(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U31(mark(z0), z1), x1, x2)), MARK(U51(U31(z0, z1), x1, x2))) A__U61(tt, U51(U32(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U32(mark(z0)), x1, x2)), MARK(U51(U32(z0), x1, x2))) A__U61(tt, U51(U41(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U51(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U51(U41(z0, z1, z2), x1, x2))) A__U61(tt, U51(U42(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U42(mark(z0), z1), x1, x2)), MARK(U51(U42(z0, z1), x1, x2))) A__U61(tt, U51(U43(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U43(mark(z0)), x1, x2)), MARK(U51(U43(z0), x1, x2))) A__U61(tt, U51(isNatIList(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatIList(z0), x1, x2)), MARK(U51(isNatIList(z0), x1, x2))) A__U61(tt, U51(U51(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U51(a__U51(mark(z0), z1, z2), x1, x2)), MARK(U51(U51(z0, z1, z2), x1, x2))) A__U61(tt, U51(U52(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U52(mark(z0), z1), x1, x2)), MARK(U51(U52(z0, z1), x1, x2))) A__U61(tt, U51(U53(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U53(mark(z0)), x1, x2)), MARK(U51(U53(z0), x1, x2))) A__U61(tt, U51(U61(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U61(mark(z0), z1), x1, x2)), MARK(U51(U61(z0, z1), x1, x2))) A__U61(tt, U51(length(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__length(mark(z0)), x1, x2)), MARK(U51(length(z0), x1, x2))) A__U61(tt, U51(and(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__and(mark(z0), z1), x1, x2)), MARK(U51(and(z0, z1), x1, x2))) A__U61(tt, U51(isNatIListKind(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatIListKind(z0), x1, x2)), MARK(U51(isNatIListKind(z0), x1, x2))) A__U61(tt, U51(isNatKind(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatKind(z0), x1, x2)), MARK(U51(isNatKind(z0), x1, x2))) A__U61(tt, U51(cons(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(cons(mark(z0), z1), x1, x2)), MARK(U51(cons(z0, z1), x1, x2))) A__U61(tt, U51(tt, x1, x2)) -> c26(A__LENGTH(a__U51(tt, x1, x2)), MARK(U51(tt, x1, x2))) A__U61(tt, U51(s(z0), x1, x2)) -> c26(A__LENGTH(a__U51(s(mark(z0)), x1, x2)), MARK(U51(s(z0), x1, x2))) A__U61(tt, U51(x0, z1, z2)) -> c26(MARK(U51(x0, z1, z2))) A__U61(tt, U51(0, x1, x2)) -> c26(A__LENGTH(a__U51(0, x1, x2))) A__U61(tt, U51(nil, x1, x2)) -> c26(A__LENGTH(a__U51(nil, x1, x2))) A__U61(tt, U52(x0, z1)) -> c26(A__LENGTH(U52(mark(x0), z1)), MARK(U52(x0, z1))) A__U61(tt, U52(zeros, x1)) -> c26(A__LENGTH(a__U52(a__zeros, x1)), MARK(U52(zeros, x1))) A__U61(tt, U52(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U11(mark(z0), z1), x1)), MARK(U52(U11(z0, z1), x1))) A__U61(tt, U52(U12(z0), x1)) -> c26(A__LENGTH(a__U52(a__U12(mark(z0)), x1)), MARK(U52(U12(z0), x1))) A__U61(tt, U52(isNatList(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatList(z0), x1)), MARK(U52(isNatList(z0), x1))) A__U61(tt, U52(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U21(mark(z0), z1), x1)), MARK(U52(U21(z0, z1), x1))) A__U61(tt, U52(U22(z0), x1)) -> c26(A__LENGTH(a__U52(a__U22(mark(z0)), x1)), MARK(U52(U22(z0), x1))) A__U61(tt, U52(isNat(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNat(z0), x1)), MARK(U52(isNat(z0), x1))) A__U61(tt, U52(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U31(mark(z0), z1), x1)), MARK(U52(U31(z0, z1), x1))) A__U61(tt, U52(U32(z0), x1)) -> c26(A__LENGTH(a__U52(a__U32(mark(z0)), x1)), MARK(U52(U32(z0), x1))) A__U61(tt, U52(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U52(a__U41(mark(z0), z1, z2), x1)), MARK(U52(U41(z0, z1, z2), x1))) A__U61(tt, U52(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U42(mark(z0), z1), x1)), MARK(U52(U42(z0, z1), x1))) A__U61(tt, U52(U43(z0), x1)) -> c26(A__LENGTH(a__U52(a__U43(mark(z0)), x1)), MARK(U52(U43(z0), x1))) A__U61(tt, U52(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatIList(z0), x1)), MARK(U52(isNatIList(z0), x1))) A__U61(tt, U52(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U52(a__U51(mark(z0), z1, z2), x1)), MARK(U52(U51(z0, z1, z2), x1))) A__U61(tt, U52(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U52(mark(z0), z1), x1)), MARK(U52(U52(z0, z1), x1))) A__U61(tt, U52(U53(z0), x1)) -> c26(A__LENGTH(a__U52(a__U53(mark(z0)), x1)), MARK(U52(U53(z0), x1))) A__U61(tt, U52(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U61(mark(z0), z1), x1)), MARK(U52(U61(z0, z1), x1))) A__U61(tt, U52(length(z0), x1)) -> c26(A__LENGTH(a__U52(a__length(mark(z0)), x1)), MARK(U52(length(z0), x1))) A__U61(tt, U52(and(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__and(mark(z0), z1), x1)), MARK(U52(and(z0, z1), x1))) A__U61(tt, U52(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatIListKind(z0), x1)), MARK(U52(isNatIListKind(z0), x1))) A__U61(tt, U52(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatKind(z0), x1)), MARK(U52(isNatKind(z0), x1))) A__U61(tt, U52(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U52(cons(mark(z0), z1), x1)), MARK(U52(cons(z0, z1), x1))) A__U61(tt, U52(0, x1)) -> c26(A__LENGTH(a__U52(0, x1)), MARK(U52(0, x1))) A__U61(tt, U52(tt, x1)) -> c26(A__LENGTH(a__U52(tt, x1)), MARK(U52(tt, x1))) A__U61(tt, U52(s(z0), x1)) -> c26(A__LENGTH(a__U52(s(mark(z0)), x1)), MARK(U52(s(z0), x1))) A__U61(tt, U52(nil, x1)) -> c26(A__LENGTH(a__U52(nil, x1)), MARK(U52(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_1, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c14_2, c20_2 ---------------------------------------- (201) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> c26(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U61(tt, U12(U21(z0, z1))) -> c26(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U61(tt, U12(U22(z0))) -> c26(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U61(tt, U12(isNat(z0))) -> c26(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U61(tt, U12(U31(z0, z1))) -> c26(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U61(tt, U12(U32(z0))) -> c26(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U61(tt, U12(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U61(tt, U12(U42(z0, z1))) -> c26(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U61(tt, U12(U43(z0))) -> c26(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U61(tt, U12(isNatIList(z0))) -> c26(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U61(tt, U12(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U61(tt, U12(U52(z0, z1))) -> c26(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U61(tt, U12(U53(z0))) -> c26(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U61(tt, U12(U61(z0, z1))) -> c26(A__LENGTH(a__U12(a__U61(mark(z0), z1))), MARK(U12(U61(z0, z1)))) A__U61(tt, U12(length(z0))) -> c26(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U61(tt, U12(and(z0, z1))) -> c26(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U61(tt, U12(isNatIListKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U61(tt, U12(isNatKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U61(tt, U12(cons(z0, z1))) -> c26(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U61(tt, U12(0)) -> c26(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U61(tt, U12(tt)) -> c26(A__LENGTH(a__U12(tt)), 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A__U61(tt, U41(tt, x1, x2)) -> c26(A__LENGTH(a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2))) A__U61(tt, U41(s(z0), x1, x2)) -> c26(A__LENGTH(a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2))) A__U61(tt, U41(x0, z1, z2)) -> c26(MARK(U41(x0, z1, z2))) A__U61(tt, U41(0, x1, x2)) -> c26(A__LENGTH(a__U41(0, x1, x2))) A__U61(tt, U41(nil, x1, x2)) -> c26(A__LENGTH(a__U41(nil, x1, x2))) A__U61(tt, U42(zeros, x1)) -> c26(A__LENGTH(a__U42(a__zeros, x1)), MARK(U42(zeros, x1))) A__U61(tt, U42(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U11(mark(z0), z1), x1)), MARK(U42(U11(z0, z1), x1))) A__U61(tt, U42(U12(z0), x1)) -> c26(A__LENGTH(a__U42(a__U12(mark(z0)), x1)), MARK(U42(U12(z0), x1))) A__U61(tt, U42(isNatList(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatList(z0), x1)), MARK(U42(isNatList(z0), x1))) A__U61(tt, U42(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U21(mark(z0), z1), x1)), MARK(U42(U21(z0, z1), x1))) A__U61(tt, U42(U22(z0), x1)) -> c26(A__LENGTH(a__U42(a__U22(mark(z0)), x1)), 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A__U61(tt, U42(x0, z1)) -> c26(MARK(U42(x0, z1))) A__U61(tt, U42(0, x1)) -> c26(A__LENGTH(a__U42(0, x1))) A__U61(tt, U42(nil, x1)) -> c26(A__LENGTH(a__U42(nil, x1))) A__U61(tt, U43(zeros)) -> c26(A__LENGTH(a__U43(a__zeros)), MARK(U43(zeros))) A__U61(tt, U43(U11(z0, z1))) -> c26(A__LENGTH(a__U43(a__U11(mark(z0), z1))), MARK(U43(U11(z0, z1)))) A__U61(tt, U43(U12(z0))) -> c26(A__LENGTH(a__U43(a__U12(mark(z0)))), MARK(U43(U12(z0)))) A__U61(tt, U43(isNatList(z0))) -> c26(A__LENGTH(a__U43(a__isNatList(z0))), MARK(U43(isNatList(z0)))) A__U61(tt, U43(U21(z0, z1))) -> c26(A__LENGTH(a__U43(a__U21(mark(z0), z1))), MARK(U43(U21(z0, z1)))) A__U61(tt, U43(U22(z0))) -> c26(A__LENGTH(a__U43(a__U22(mark(z0)))), MARK(U43(U22(z0)))) A__U61(tt, U43(isNat(z0))) -> c26(A__LENGTH(a__U43(a__isNat(z0))), MARK(U43(isNat(z0)))) A__U61(tt, U43(U31(z0, z1))) -> c26(A__LENGTH(a__U43(a__U31(mark(z0), z1))), MARK(U43(U31(z0, z1)))) A__U61(tt, U43(U32(z0))) -> c26(A__LENGTH(a__U43(a__U32(mark(z0)))), MARK(U43(U32(z0)))) A__U61(tt, U43(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U43(a__U41(mark(z0), z1, z2))), MARK(U43(U41(z0, z1, z2)))) A__U61(tt, U43(U42(z0, z1))) -> c26(A__LENGTH(a__U43(a__U42(mark(z0), z1))), MARK(U43(U42(z0, z1)))) A__U61(tt, U43(U43(z0))) -> c26(A__LENGTH(a__U43(a__U43(mark(z0)))), MARK(U43(U43(z0)))) A__U61(tt, U43(isNatIList(z0))) -> c26(A__LENGTH(a__U43(a__isNatIList(z0))), MARK(U43(isNatIList(z0)))) A__U61(tt, U43(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U43(a__U51(mark(z0), z1, z2))), MARK(U43(U51(z0, z1, z2)))) A__U61(tt, U43(U52(z0, z1))) -> c26(A__LENGTH(a__U43(a__U52(mark(z0), z1))), MARK(U43(U52(z0, z1)))) A__U61(tt, U43(U53(z0))) -> c26(A__LENGTH(a__U43(a__U53(mark(z0)))), MARK(U43(U53(z0)))) A__U61(tt, U43(U61(z0, z1))) -> c26(A__LENGTH(a__U43(a__U61(mark(z0), z1))), MARK(U43(U61(z0, z1)))) A__U61(tt, U43(length(z0))) -> c26(A__LENGTH(a__U43(a__length(mark(z0)))), MARK(U43(length(z0)))) A__U61(tt, U43(and(z0, z1))) -> c26(A__LENGTH(a__U43(a__and(mark(z0), 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isNatIList(z0)) -> c26(MARK(isNatIList(z0))) A__U61(tt, U51(zeros, x1, x2)) -> c26(A__LENGTH(a__U51(a__zeros, x1, x2)), MARK(U51(zeros, x1, x2))) A__U61(tt, U51(U11(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U11(mark(z0), z1), x1, x2)), MARK(U51(U11(z0, z1), x1, x2))) A__U61(tt, U51(U12(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U12(mark(z0)), x1, x2)), MARK(U51(U12(z0), x1, x2))) A__U61(tt, U51(isNatList(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatList(z0), x1, x2)), MARK(U51(isNatList(z0), x1, x2))) A__U61(tt, U51(U21(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U21(mark(z0), z1), x1, x2)), MARK(U51(U21(z0, z1), x1, x2))) A__U61(tt, U51(U22(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U22(mark(z0)), x1, x2)), MARK(U51(U22(z0), x1, x2))) A__U61(tt, U51(isNat(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNat(z0), x1, x2)), MARK(U51(isNat(z0), x1, x2))) A__U61(tt, U51(U31(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U31(mark(z0), z1), x1, x2)), MARK(U51(U31(z0, z1), x1, x2))) A__U61(tt, U51(U32(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U32(mark(z0)), x1, x2)), MARK(U51(U32(z0), x1, x2))) A__U61(tt, U51(U41(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U51(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U51(U41(z0, z1, z2), x1, x2))) A__U61(tt, U51(U42(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U42(mark(z0), z1), x1, x2)), MARK(U51(U42(z0, z1), x1, x2))) A__U61(tt, U51(U43(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U43(mark(z0)), x1, x2)), MARK(U51(U43(z0), x1, x2))) A__U61(tt, U51(isNatIList(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatIList(z0), x1, x2)), MARK(U51(isNatIList(z0), x1, x2))) A__U61(tt, U51(U51(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U51(a__U51(mark(z0), z1, z2), x1, x2)), MARK(U51(U51(z0, z1, z2), x1, x2))) A__U61(tt, U51(U52(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U52(mark(z0), z1), x1, x2)), MARK(U51(U52(z0, z1), x1, x2))) A__U61(tt, U51(U53(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U53(mark(z0)), x1, x2)), MARK(U51(U53(z0), x1, x2))) A__U61(tt, U51(U61(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U61(mark(z0), z1), x1, x2)), MARK(U51(U61(z0, z1), x1, x2))) A__U61(tt, U51(length(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__length(mark(z0)), x1, x2)), MARK(U51(length(z0), x1, x2))) A__U61(tt, U51(and(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__and(mark(z0), z1), x1, x2)), MARK(U51(and(z0, z1), x1, x2))) A__U61(tt, U51(isNatIListKind(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatIListKind(z0), x1, x2)), MARK(U51(isNatIListKind(z0), x1, x2))) A__U61(tt, U51(isNatKind(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatKind(z0), x1, x2)), MARK(U51(isNatKind(z0), x1, x2))) A__U61(tt, U51(cons(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(cons(mark(z0), z1), x1, x2)), MARK(U51(cons(z0, z1), x1, x2))) A__U61(tt, U51(tt, x1, x2)) -> c26(A__LENGTH(a__U51(tt, x1, x2)), MARK(U51(tt, x1, x2))) A__U61(tt, U51(s(z0), x1, x2)) -> c26(A__LENGTH(a__U51(s(mark(z0)), x1, x2)), MARK(U51(s(z0), x1, x2))) A__U61(tt, U51(x0, z1, z2)) -> c26(MARK(U51(x0, z1, z2))) A__U61(tt, U51(0, x1, x2)) -> c26(A__LENGTH(a__U51(0, x1, x2))) A__U61(tt, U51(nil, x1, x2)) -> c26(A__LENGTH(a__U51(nil, x1, x2))) A__U61(tt, U52(zeros, x1)) -> c26(A__LENGTH(a__U52(a__zeros, x1)), MARK(U52(zeros, x1))) A__U61(tt, U52(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U11(mark(z0), z1), x1)), MARK(U52(U11(z0, z1), x1))) A__U61(tt, U52(U12(z0), x1)) -> c26(A__LENGTH(a__U52(a__U12(mark(z0)), x1)), MARK(U52(U12(z0), x1))) A__U61(tt, U52(isNatList(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatList(z0), x1)), MARK(U52(isNatList(z0), x1))) A__U61(tt, U52(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U21(mark(z0), z1), x1)), MARK(U52(U21(z0, z1), x1))) A__U61(tt, U52(U22(z0), x1)) -> c26(A__LENGTH(a__U52(a__U22(mark(z0)), x1)), MARK(U52(U22(z0), x1))) A__U61(tt, U52(isNat(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNat(z0), x1)), MARK(U52(isNat(z0), x1))) A__U61(tt, U52(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U31(mark(z0), z1), x1)), MARK(U52(U31(z0, z1), x1))) A__U61(tt, U52(U32(z0), x1)) -> c26(A__LENGTH(a__U52(a__U32(mark(z0)), x1)), MARK(U52(U32(z0), x1))) A__U61(tt, U52(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U52(a__U41(mark(z0), z1, z2), x1)), MARK(U52(U41(z0, z1, z2), x1))) A__U61(tt, U52(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U42(mark(z0), z1), x1)), MARK(U52(U42(z0, z1), x1))) A__U61(tt, U52(U43(z0), x1)) -> c26(A__LENGTH(a__U52(a__U43(mark(z0)), x1)), MARK(U52(U43(z0), x1))) A__U61(tt, U52(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatIList(z0), x1)), MARK(U52(isNatIList(z0), x1))) A__U61(tt, U52(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U52(a__U51(mark(z0), z1, z2), x1)), MARK(U52(U51(z0, z1, z2), x1))) A__U61(tt, U52(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U52(mark(z0), z1), x1)), MARK(U52(U52(z0, z1), x1))) A__U61(tt, U52(U53(z0), x1)) -> c26(A__LENGTH(a__U52(a__U53(mark(z0)), x1)), MARK(U52(U53(z0), x1))) A__U61(tt, U52(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U61(mark(z0), z1), x1)), MARK(U52(U61(z0, z1), x1))) A__U61(tt, U52(length(z0), x1)) -> c26(A__LENGTH(a__U52(a__length(mark(z0)), x1)), MARK(U52(length(z0), x1))) A__U61(tt, U52(and(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__and(mark(z0), z1), x1)), MARK(U52(and(z0, z1), x1))) A__U61(tt, U52(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatIListKind(z0), x1)), MARK(U52(isNatIListKind(z0), x1))) A__U61(tt, U52(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatKind(z0), x1)), MARK(U52(isNatKind(z0), x1))) A__U61(tt, U52(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U52(cons(mark(z0), z1), x1)), MARK(U52(cons(z0, z1), x1))) A__U61(tt, U52(tt, x1)) -> c26(A__LENGTH(a__U52(tt, x1)), MARK(U52(tt, x1))) A__U61(tt, U52(s(z0), x1)) -> c26(A__LENGTH(a__U52(s(mark(z0)), x1)), MARK(U52(s(z0), x1))) A__U61(tt, U52(x0, z1)) -> c26(MARK(U52(x0, z1))) A__U61(tt, U52(0, x1)) -> c26(A__LENGTH(a__U52(0, x1))) A__U61(tt, U52(nil, x1)) -> c26(A__LENGTH(a__U52(nil, x1))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> c26(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U61(tt, U12(U21(z0, z1))) -> c26(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U61(tt, U12(U22(z0))) -> c26(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U61(tt, U12(isNat(z0))) -> c26(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U61(tt, U12(U31(z0, z1))) -> c26(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U61(tt, U12(U32(z0))) -> c26(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U61(tt, U12(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U61(tt, U12(U42(z0, z1))) -> c26(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U61(tt, U12(U43(z0))) -> c26(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U61(tt, U12(isNatIList(z0))) -> c26(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U61(tt, U12(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U61(tt, U12(U52(z0, z1))) -> c26(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U61(tt, U12(U53(z0))) -> c26(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U61(tt, U12(U61(z0, z1))) -> c26(A__LENGTH(a__U12(a__U61(mark(z0), z1))), MARK(U12(U61(z0, z1)))) A__U61(tt, U12(length(z0))) -> c26(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U61(tt, U12(and(z0, z1))) -> c26(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U61(tt, U12(isNatIListKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U61(tt, U12(isNatKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U61(tt, U12(cons(z0, z1))) -> c26(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U61(tt, U12(0)) -> c26(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U61(tt, U12(tt)) -> c26(A__LENGTH(a__U12(tt)), MARK(U12(tt))) A__U61(tt, U12(s(z0))) -> c26(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U61(tt, U12(nil)) -> c26(A__LENGTH(a__U12(nil)), MARK(U12(nil))) A__U61(tt, U12(x0)) -> c26(MARK(U12(x0))) A__U61(tt, isNatList(cons(z0, z1))) -> c26(A__LENGTH(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(cons(z0, z1)))) A__U61(tt, isNatList(nil)) -> c26(MARK(isNatList(nil))) A__U61(tt, isNatList(z0)) -> c26(MARK(isNatList(z0))) A__U61(tt, U21(zeros, x1)) -> c26(A__LENGTH(a__U21(a__zeros, x1)), MARK(U21(zeros, x1))) A__U61(tt, U21(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1)), MARK(U21(U11(z0, z1), x1))) A__U61(tt, U21(U12(z0), x1)) -> c26(A__LENGTH(a__U21(a__U12(mark(z0)), x1)), MARK(U21(U12(z0), x1))) A__U61(tt, U21(isNatList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatList(z0), x1)), MARK(U21(isNatList(z0), x1))) A__U61(tt, U21(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U21(mark(z0), z1), x1)), MARK(U21(U21(z0, z1), x1))) A__U61(tt, U21(U22(z0), x1)) -> c26(A__LENGTH(a__U21(a__U22(mark(z0)), x1)), MARK(U21(U22(z0), x1))) A__U61(tt, U21(isNat(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNat(z0), x1)), MARK(U21(isNat(z0), x1))) A__U61(tt, U21(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U31(mark(z0), z1), x1)), MARK(U21(U31(z0, z1), x1))) A__U61(tt, U21(U32(z0), x1)) -> c26(A__LENGTH(a__U21(a__U32(mark(z0)), x1)), MARK(U21(U32(z0), x1))) A__U61(tt, U21(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(U21(U41(z0, z1, z2), x1))) A__U61(tt, U21(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U42(mark(z0), z1), x1)), MARK(U21(U42(z0, z1), x1))) A__U61(tt, U21(U43(z0), x1)) -> c26(A__LENGTH(a__U21(a__U43(mark(z0)), x1)), MARK(U21(U43(z0), x1))) A__U61(tt, U21(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIList(z0), x1)), MARK(U21(isNatIList(z0), x1))) A__U61(tt, U21(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U51(mark(z0), z1, z2), x1)), MARK(U21(U51(z0, z1, z2), x1))) A__U61(tt, U21(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U52(mark(z0), z1), x1)), MARK(U21(U52(z0, z1), x1))) 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A__U61(tt, U41(s(z0), x1, x2)) -> c26(A__LENGTH(a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2))) A__U61(tt, U41(x0, z1, z2)) -> c26(MARK(U41(x0, z1, z2))) A__U61(tt, U41(0, x1, x2)) -> c26(A__LENGTH(a__U41(0, x1, x2))) A__U61(tt, U41(nil, x1, x2)) -> c26(A__LENGTH(a__U41(nil, x1, x2))) A__U61(tt, U42(zeros, x1)) -> c26(A__LENGTH(a__U42(a__zeros, x1)), MARK(U42(zeros, x1))) A__U61(tt, U42(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U11(mark(z0), z1), x1)), MARK(U42(U11(z0, z1), x1))) A__U61(tt, U42(U12(z0), x1)) -> c26(A__LENGTH(a__U42(a__U12(mark(z0)), x1)), MARK(U42(U12(z0), x1))) A__U61(tt, U42(isNatList(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatList(z0), x1)), MARK(U42(isNatList(z0), x1))) A__U61(tt, U42(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U21(mark(z0), z1), x1)), MARK(U42(U21(z0, z1), x1))) A__U61(tt, U42(U22(z0), x1)) -> c26(A__LENGTH(a__U42(a__U22(mark(z0)), x1)), MARK(U42(U22(z0), x1))) A__U61(tt, U42(isNat(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNat(z0), x1)), MARK(U42(isNat(z0), x1))) A__U61(tt, U42(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U31(mark(z0), z1), x1)), MARK(U42(U31(z0, z1), x1))) A__U61(tt, U42(U32(z0), x1)) -> c26(A__LENGTH(a__U42(a__U32(mark(z0)), x1)), MARK(U42(U32(z0), x1))) A__U61(tt, U42(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U42(a__U41(mark(z0), z1, z2), x1)), MARK(U42(U41(z0, z1, z2), x1))) A__U61(tt, U42(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U42(mark(z0), z1), x1)), MARK(U42(U42(z0, z1), x1))) A__U61(tt, U42(U43(z0), x1)) -> c26(A__LENGTH(a__U42(a__U43(mark(z0)), x1)), MARK(U42(U43(z0), x1))) A__U61(tt, U42(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatIList(z0), x1)), MARK(U42(isNatIList(z0), x1))) A__U61(tt, U42(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U42(a__U51(mark(z0), z1, z2), x1)), MARK(U42(U51(z0, z1, z2), x1))) A__U61(tt, U42(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U52(mark(z0), z1), x1)), MARK(U42(U52(z0, z1), x1))) A__U61(tt, U42(U53(z0), x1)) -> c26(A__LENGTH(a__U42(a__U53(mark(z0)), x1)), MARK(U42(U53(z0), x1))) A__U61(tt, U42(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U61(mark(z0), z1), x1)), MARK(U42(U61(z0, z1), x1))) A__U61(tt, U42(length(z0), x1)) -> c26(A__LENGTH(a__U42(a__length(mark(z0)), x1)), MARK(U42(length(z0), x1))) A__U61(tt, U42(and(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__and(mark(z0), z1), x1)), MARK(U42(and(z0, z1), x1))) A__U61(tt, U42(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatIListKind(z0), x1)), MARK(U42(isNatIListKind(z0), x1))) A__U61(tt, U42(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatKind(z0), x1)), MARK(U42(isNatKind(z0), x1))) A__U61(tt, U42(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U42(cons(mark(z0), z1), x1)), MARK(U42(cons(z0, z1), x1))) A__U61(tt, U42(tt, x1)) -> c26(A__LENGTH(a__U42(tt, x1)), MARK(U42(tt, x1))) A__U61(tt, U42(s(z0), x1)) -> c26(A__LENGTH(a__U42(s(mark(z0)), x1)), MARK(U42(s(z0), x1))) A__U61(tt, U42(x0, z1)) -> c26(MARK(U42(x0, z1))) A__U61(tt, U42(0, x1)) -> c26(A__LENGTH(a__U42(0, x1))) A__U61(tt, U42(nil, x1)) -> c26(A__LENGTH(a__U42(nil, x1))) A__U61(tt, U43(zeros)) -> c26(A__LENGTH(a__U43(a__zeros)), MARK(U43(zeros))) A__U61(tt, U43(U11(z0, z1))) -> c26(A__LENGTH(a__U43(a__U11(mark(z0), z1))), MARK(U43(U11(z0, z1)))) A__U61(tt, U43(U12(z0))) -> c26(A__LENGTH(a__U43(a__U12(mark(z0)))), MARK(U43(U12(z0)))) A__U61(tt, U43(isNatList(z0))) -> c26(A__LENGTH(a__U43(a__isNatList(z0))), MARK(U43(isNatList(z0)))) A__U61(tt, U43(U21(z0, z1))) -> c26(A__LENGTH(a__U43(a__U21(mark(z0), z1))), MARK(U43(U21(z0, z1)))) A__U61(tt, U43(U22(z0))) -> c26(A__LENGTH(a__U43(a__U22(mark(z0)))), MARK(U43(U22(z0)))) A__U61(tt, U43(isNat(z0))) -> c26(A__LENGTH(a__U43(a__isNat(z0))), MARK(U43(isNat(z0)))) A__U61(tt, U43(U31(z0, z1))) -> c26(A__LENGTH(a__U43(a__U31(mark(z0), z1))), MARK(U43(U31(z0, z1)))) A__U61(tt, U43(U32(z0))) -> c26(A__LENGTH(a__U43(a__U32(mark(z0)))), MARK(U43(U32(z0)))) A__U61(tt, U43(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U43(a__U41(mark(z0), z1, z2))), MARK(U43(U41(z0, z1, z2)))) A__U61(tt, U43(U42(z0, z1))) -> c26(A__LENGTH(a__U43(a__U42(mark(z0), z1))), MARK(U43(U42(z0, z1)))) A__U61(tt, U43(U43(z0))) -> c26(A__LENGTH(a__U43(a__U43(mark(z0)))), MARK(U43(U43(z0)))) A__U61(tt, U43(isNatIList(z0))) -> c26(A__LENGTH(a__U43(a__isNatIList(z0))), MARK(U43(isNatIList(z0)))) A__U61(tt, U43(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U43(a__U51(mark(z0), z1, z2))), MARK(U43(U51(z0, z1, z2)))) A__U61(tt, U43(U52(z0, z1))) -> c26(A__LENGTH(a__U43(a__U52(mark(z0), z1))), MARK(U43(U52(z0, z1)))) A__U61(tt, U43(U53(z0))) -> c26(A__LENGTH(a__U43(a__U53(mark(z0)))), MARK(U43(U53(z0)))) A__U61(tt, U43(U61(z0, z1))) -> c26(A__LENGTH(a__U43(a__U61(mark(z0), z1))), MARK(U43(U61(z0, z1)))) A__U61(tt, U43(length(z0))) -> c26(A__LENGTH(a__U43(a__length(mark(z0)))), MARK(U43(length(z0)))) A__U61(tt, U43(and(z0, z1))) -> c26(A__LENGTH(a__U43(a__and(mark(z0), z1))), MARK(U43(and(z0, z1)))) A__U61(tt, U43(isNatIListKind(z0))) -> c26(A__LENGTH(a__U43(a__isNatIListKind(z0))), MARK(U43(isNatIListKind(z0)))) A__U61(tt, U43(isNatKind(z0))) -> c26(A__LENGTH(a__U43(a__isNatKind(z0))), MARK(U43(isNatKind(z0)))) A__U61(tt, U43(cons(z0, z1))) -> c26(A__LENGTH(a__U43(cons(mark(z0), z1))), MARK(U43(cons(z0, z1)))) A__U61(tt, U43(0)) -> c26(A__LENGTH(a__U43(0)), MARK(U43(0))) A__U61(tt, U43(tt)) -> c26(A__LENGTH(a__U43(tt)), MARK(U43(tt))) A__U61(tt, U43(s(z0))) -> c26(A__LENGTH(a__U43(s(mark(z0)))), MARK(U43(s(z0)))) A__U61(tt, U43(nil)) -> c26(A__LENGTH(a__U43(nil)), MARK(U43(nil))) A__U61(tt, U43(x0)) -> c26(MARK(U43(x0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__U31(a__isNatIListKind(z0), z0)), MARK(isNatIList(z0))) A__U61(tt, isNatIList(cons(z0, z1))) -> c26(A__LENGTH(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatIList(cons(z0, z1)))) A__U61(tt, isNatIList(zeros)) -> c26(MARK(isNatIList(zeros))) A__U61(tt, isNatIList(z0)) -> c26(MARK(isNatIList(z0))) A__U61(tt, U51(zeros, x1, x2)) -> c26(A__LENGTH(a__U51(a__zeros, x1, x2)), MARK(U51(zeros, x1, x2))) A__U61(tt, U51(U11(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U11(mark(z0), z1), x1, x2)), MARK(U51(U11(z0, z1), x1, x2))) A__U61(tt, U51(U12(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U12(mark(z0)), x1, x2)), MARK(U51(U12(z0), x1, x2))) A__U61(tt, U51(isNatList(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatList(z0), x1, x2)), MARK(U51(isNatList(z0), x1, x2))) A__U61(tt, U51(U21(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U21(mark(z0), z1), x1, x2)), MARK(U51(U21(z0, z1), x1, x2))) A__U61(tt, U51(U22(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U22(mark(z0)), x1, x2)), MARK(U51(U22(z0), x1, x2))) A__U61(tt, U51(isNat(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNat(z0), x1, x2)), MARK(U51(isNat(z0), x1, x2))) A__U61(tt, U51(U31(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U31(mark(z0), z1), x1, x2)), MARK(U51(U31(z0, z1), x1, x2))) A__U61(tt, U51(U32(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U32(mark(z0)), x1, x2)), MARK(U51(U32(z0), x1, x2))) A__U61(tt, U51(U41(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U51(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U51(U41(z0, z1, z2), x1, x2))) A__U61(tt, U51(U42(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U42(mark(z0), z1), x1, x2)), MARK(U51(U42(z0, z1), x1, x2))) A__U61(tt, U51(U43(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U43(mark(z0)), x1, x2)), MARK(U51(U43(z0), x1, x2))) A__U61(tt, U51(isNatIList(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatIList(z0), x1, x2)), MARK(U51(isNatIList(z0), x1, x2))) A__U61(tt, U51(U51(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U51(a__U51(mark(z0), z1, z2), x1, x2)), MARK(U51(U51(z0, z1, z2), x1, x2))) A__U61(tt, U51(U52(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U52(mark(z0), z1), x1, x2)), MARK(U51(U52(z0, z1), x1, x2))) A__U61(tt, U51(U53(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U53(mark(z0)), x1, x2)), MARK(U51(U53(z0), x1, x2))) A__U61(tt, U51(U61(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U61(mark(z0), z1), x1, x2)), MARK(U51(U61(z0, z1), x1, x2))) A__U61(tt, U51(length(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__length(mark(z0)), x1, x2)), MARK(U51(length(z0), x1, x2))) A__U61(tt, U51(and(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__and(mark(z0), z1), x1, x2)), MARK(U51(and(z0, z1), x1, x2))) A__U61(tt, U51(isNatIListKind(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatIListKind(z0), x1, x2)), MARK(U51(isNatIListKind(z0), x1, x2))) A__U61(tt, U51(isNatKind(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatKind(z0), x1, x2)), MARK(U51(isNatKind(z0), x1, x2))) A__U61(tt, U51(cons(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(cons(mark(z0), z1), x1, x2)), MARK(U51(cons(z0, z1), x1, x2))) A__U61(tt, U51(tt, x1, x2)) -> c26(A__LENGTH(a__U51(tt, x1, x2)), MARK(U51(tt, x1, x2))) A__U61(tt, U51(s(z0), x1, x2)) -> c26(A__LENGTH(a__U51(s(mark(z0)), x1, x2)), MARK(U51(s(z0), x1, x2))) A__U61(tt, U51(x0, z1, z2)) -> c26(MARK(U51(x0, z1, z2))) A__U61(tt, U51(0, x1, x2)) -> c26(A__LENGTH(a__U51(0, x1, x2))) A__U61(tt, U51(nil, x1, x2)) -> c26(A__LENGTH(a__U51(nil, x1, x2))) A__U61(tt, U52(zeros, x1)) -> c26(A__LENGTH(a__U52(a__zeros, x1)), MARK(U52(zeros, x1))) A__U61(tt, U52(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U11(mark(z0), z1), x1)), MARK(U52(U11(z0, z1), x1))) A__U61(tt, U52(U12(z0), x1)) -> c26(A__LENGTH(a__U52(a__U12(mark(z0)), x1)), MARK(U52(U12(z0), x1))) A__U61(tt, U52(isNatList(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatList(z0), x1)), MARK(U52(isNatList(z0), x1))) A__U61(tt, U52(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U21(mark(z0), z1), x1)), MARK(U52(U21(z0, z1), x1))) A__U61(tt, U52(U22(z0), x1)) -> c26(A__LENGTH(a__U52(a__U22(mark(z0)), x1)), MARK(U52(U22(z0), x1))) A__U61(tt, U52(isNat(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNat(z0), x1)), MARK(U52(isNat(z0), x1))) A__U61(tt, U52(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U31(mark(z0), z1), x1)), MARK(U52(U31(z0, z1), x1))) A__U61(tt, U52(U32(z0), x1)) -> c26(A__LENGTH(a__U52(a__U32(mark(z0)), x1)), MARK(U52(U32(z0), x1))) A__U61(tt, U52(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U52(a__U41(mark(z0), z1, z2), x1)), MARK(U52(U41(z0, z1, z2), x1))) A__U61(tt, U52(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U42(mark(z0), z1), x1)), MARK(U52(U42(z0, z1), x1))) A__U61(tt, U52(U43(z0), x1)) -> c26(A__LENGTH(a__U52(a__U43(mark(z0)), x1)), MARK(U52(U43(z0), x1))) A__U61(tt, U52(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatIList(z0), x1)), MARK(U52(isNatIList(z0), x1))) A__U61(tt, U52(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U52(a__U51(mark(z0), z1, z2), x1)), MARK(U52(U51(z0, z1, z2), x1))) A__U61(tt, U52(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U52(mark(z0), z1), x1)), MARK(U52(U52(z0, z1), x1))) A__U61(tt, U52(U53(z0), x1)) -> c26(A__LENGTH(a__U52(a__U53(mark(z0)), x1)), MARK(U52(U53(z0), x1))) A__U61(tt, U52(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U61(mark(z0), z1), x1)), MARK(U52(U61(z0, z1), x1))) A__U61(tt, U52(length(z0), x1)) -> c26(A__LENGTH(a__U52(a__length(mark(z0)), x1)), MARK(U52(length(z0), x1))) A__U61(tt, U52(and(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__and(mark(z0), z1), x1)), MARK(U52(and(z0, z1), x1))) A__U61(tt, U52(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatIListKind(z0), x1)), MARK(U52(isNatIListKind(z0), x1))) A__U61(tt, U52(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatKind(z0), x1)), MARK(U52(isNatKind(z0), x1))) A__U61(tt, U52(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U52(cons(mark(z0), z1), x1)), MARK(U52(cons(z0, z1), x1))) A__U61(tt, U52(tt, x1)) -> c26(A__LENGTH(a__U52(tt, x1)), MARK(U52(tt, x1))) A__U61(tt, U52(s(z0), x1)) -> c26(A__LENGTH(a__U52(s(mark(z0)), x1)), MARK(U52(s(z0), x1))) A__U61(tt, U52(x0, z1)) -> c26(MARK(U52(x0, z1))) A__U61(tt, U52(0, x1)) -> c26(A__LENGTH(a__U52(0, x1))) A__U61(tt, U52(nil, x1)) -> c26(A__LENGTH(a__U52(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_1, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c14_2, c20_2 ---------------------------------------- (203) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U61(tt, U53(z0)) -> c26(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) by A__U61(tt, U53(x0)) -> c26(A__LENGTH(U53(mark(x0))), MARK(U53(x0))) A__U61(tt, U53(zeros)) -> c26(A__LENGTH(a__U53(a__zeros)), MARK(U53(zeros))) A__U61(tt, U53(U11(z0, z1))) -> c26(A__LENGTH(a__U53(a__U11(mark(z0), z1))), MARK(U53(U11(z0, z1)))) A__U61(tt, U53(U12(z0))) -> c26(A__LENGTH(a__U53(a__U12(mark(z0)))), MARK(U53(U12(z0)))) A__U61(tt, U53(isNatList(z0))) -> c26(A__LENGTH(a__U53(a__isNatList(z0))), MARK(U53(isNatList(z0)))) A__U61(tt, U53(U21(z0, z1))) -> c26(A__LENGTH(a__U53(a__U21(mark(z0), z1))), MARK(U53(U21(z0, z1)))) A__U61(tt, U53(U22(z0))) -> c26(A__LENGTH(a__U53(a__U22(mark(z0)))), MARK(U53(U22(z0)))) A__U61(tt, U53(isNat(z0))) -> c26(A__LENGTH(a__U53(a__isNat(z0))), MARK(U53(isNat(z0)))) A__U61(tt, U53(U31(z0, z1))) -> c26(A__LENGTH(a__U53(a__U31(mark(z0), z1))), MARK(U53(U31(z0, z1)))) A__U61(tt, U53(U32(z0))) -> c26(A__LENGTH(a__U53(a__U32(mark(z0)))), MARK(U53(U32(z0)))) A__U61(tt, U53(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U53(a__U41(mark(z0), z1, z2))), MARK(U53(U41(z0, z1, z2)))) A__U61(tt, U53(U42(z0, z1))) -> c26(A__LENGTH(a__U53(a__U42(mark(z0), z1))), MARK(U53(U42(z0, z1)))) A__U61(tt, U53(U43(z0))) -> c26(A__LENGTH(a__U53(a__U43(mark(z0)))), MARK(U53(U43(z0)))) A__U61(tt, U53(isNatIList(z0))) -> c26(A__LENGTH(a__U53(a__isNatIList(z0))), MARK(U53(isNatIList(z0)))) A__U61(tt, U53(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U53(a__U51(mark(z0), z1, z2))), MARK(U53(U51(z0, z1, z2)))) A__U61(tt, U53(U52(z0, z1))) -> c26(A__LENGTH(a__U53(a__U52(mark(z0), z1))), MARK(U53(U52(z0, z1)))) A__U61(tt, U53(U53(z0))) -> c26(A__LENGTH(a__U53(a__U53(mark(z0)))), MARK(U53(U53(z0)))) A__U61(tt, U53(U61(z0, z1))) -> c26(A__LENGTH(a__U53(a__U61(mark(z0), z1))), MARK(U53(U61(z0, z1)))) A__U61(tt, U53(length(z0))) -> c26(A__LENGTH(a__U53(a__length(mark(z0)))), MARK(U53(length(z0)))) A__U61(tt, U53(and(z0, z1))) -> c26(A__LENGTH(a__U53(a__and(mark(z0), z1))), MARK(U53(and(z0, z1)))) A__U61(tt, U53(isNatIListKind(z0))) -> c26(A__LENGTH(a__U53(a__isNatIListKind(z0))), MARK(U53(isNatIListKind(z0)))) A__U61(tt, U53(isNatKind(z0))) -> c26(A__LENGTH(a__U53(a__isNatKind(z0))), MARK(U53(isNatKind(z0)))) A__U61(tt, U53(cons(z0, z1))) -> c26(A__LENGTH(a__U53(cons(mark(z0), z1))), MARK(U53(cons(z0, z1)))) A__U61(tt, U53(0)) -> c26(A__LENGTH(a__U53(0)), MARK(U53(0))) A__U61(tt, U53(tt)) -> c26(A__LENGTH(a__U53(tt)), MARK(U53(tt))) A__U61(tt, U53(s(z0))) -> c26(A__LENGTH(a__U53(s(mark(z0)))), MARK(U53(s(z0)))) A__U61(tt, U53(nil)) -> c26(A__LENGTH(a__U53(nil)), MARK(U53(nil))) A__U61(tt, U53(x0)) -> c26(MARK(U53(x0))) ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> c26(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U61(tt, U12(U21(z0, z1))) -> c26(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U61(tt, U12(U22(z0))) -> c26(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U61(tt, U12(isNat(z0))) -> c26(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U61(tt, U12(U31(z0, z1))) -> c26(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U61(tt, U12(U32(z0))) -> c26(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U61(tt, U12(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U61(tt, U12(U42(z0, z1))) -> c26(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U61(tt, U12(U43(z0))) -> c26(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U61(tt, U12(isNatIList(z0))) -> c26(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U61(tt, U12(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U61(tt, U12(U52(z0, z1))) -> c26(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U61(tt, U12(U53(z0))) -> c26(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U61(tt, U12(U61(z0, z1))) -> c26(A__LENGTH(a__U12(a__U61(mark(z0), z1))), MARK(U12(U61(z0, z1)))) A__U61(tt, U12(length(z0))) -> c26(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U61(tt, U12(and(z0, z1))) -> c26(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U61(tt, U12(isNatIListKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U61(tt, U12(isNatKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U61(tt, U12(cons(z0, z1))) -> c26(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U61(tt, U12(0)) -> c26(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U61(tt, U12(tt)) -> c26(A__LENGTH(a__U12(tt)), MARK(U12(tt))) A__U61(tt, U12(s(z0))) -> c26(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U61(tt, U12(nil)) -> c26(A__LENGTH(a__U12(nil)), MARK(U12(nil))) A__U61(tt, U12(x0)) -> c26(MARK(U12(x0))) A__U61(tt, isNatList(cons(z0, z1))) -> c26(A__LENGTH(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(cons(z0, z1)))) A__U61(tt, isNatList(nil)) -> c26(MARK(isNatList(nil))) A__U61(tt, isNatList(z0)) -> c26(MARK(isNatList(z0))) A__U61(tt, U21(zeros, x1)) -> 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-> c26(A__LENGTH(a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2))) A__U61(tt, U41(U42(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U42(mark(z0), z1), x1, x2)), MARK(U41(U42(z0, z1), x1, x2))) A__U61(tt, U41(U43(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U43(mark(z0)), x1, x2)), MARK(U41(U43(z0), x1, x2))) A__U61(tt, U41(isNatIList(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatIList(z0), x1, x2)), MARK(U41(isNatIList(z0), x1, x2))) A__U61(tt, U41(U51(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U41(a__U51(mark(z0), z1, z2), x1, x2)), MARK(U41(U51(z0, z1, z2), x1, x2))) A__U61(tt, U41(U52(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U52(mark(z0), z1), x1, x2)), MARK(U41(U52(z0, z1), x1, x2))) A__U61(tt, U41(U53(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U53(mark(z0)), x1, x2)), MARK(U41(U53(z0), x1, x2))) A__U61(tt, U41(U61(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U61(mark(z0), z1), x1, x2)), MARK(U41(U61(z0, z1), x1, x2))) A__U61(tt, U41(length(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__length(mark(z0)), x1, x2)), MARK(U41(length(z0), x1, x2))) A__U61(tt, U41(and(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__and(mark(z0), z1), x1, x2)), MARK(U41(and(z0, z1), x1, x2))) A__U61(tt, U41(isNatIListKind(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatIListKind(z0), x1, x2)), MARK(U41(isNatIListKind(z0), x1, x2))) A__U61(tt, U41(isNatKind(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatKind(z0), x1, x2)), MARK(U41(isNatKind(z0), x1, x2))) A__U61(tt, U41(cons(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(cons(mark(z0), z1), x1, x2)), MARK(U41(cons(z0, z1), x1, x2))) A__U61(tt, U41(tt, x1, x2)) -> c26(A__LENGTH(a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2))) A__U61(tt, U41(s(z0), x1, x2)) -> c26(A__LENGTH(a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2))) A__U61(tt, U41(x0, z1, z2)) -> c26(MARK(U41(x0, z1, z2))) A__U61(tt, U41(0, x1, x2)) -> c26(A__LENGTH(a__U41(0, x1, x2))) A__U61(tt, U41(nil, x1, x2)) -> c26(A__LENGTH(a__U41(nil, x1, x2))) A__U61(tt, U42(zeros, x1)) -> c26(A__LENGTH(a__U42(a__zeros, x1)), MARK(U42(zeros, x1))) A__U61(tt, U42(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U11(mark(z0), z1), x1)), MARK(U42(U11(z0, z1), x1))) A__U61(tt, U42(U12(z0), x1)) -> c26(A__LENGTH(a__U42(a__U12(mark(z0)), x1)), MARK(U42(U12(z0), x1))) A__U61(tt, U42(isNatList(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatList(z0), x1)), MARK(U42(isNatList(z0), x1))) A__U61(tt, U42(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U21(mark(z0), z1), x1)), MARK(U42(U21(z0, z1), x1))) A__U61(tt, U42(U22(z0), x1)) -> c26(A__LENGTH(a__U42(a__U22(mark(z0)), x1)), MARK(U42(U22(z0), x1))) A__U61(tt, U42(isNat(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNat(z0), x1)), MARK(U42(isNat(z0), x1))) A__U61(tt, U42(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U31(mark(z0), z1), x1)), MARK(U42(U31(z0, z1), x1))) A__U61(tt, U42(U32(z0), x1)) -> c26(A__LENGTH(a__U42(a__U32(mark(z0)), x1)), MARK(U42(U32(z0), x1))) A__U61(tt, U42(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U42(a__U41(mark(z0), z1, z2), x1)), MARK(U42(U41(z0, z1, z2), x1))) A__U61(tt, U42(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U42(mark(z0), z1), x1)), MARK(U42(U42(z0, z1), x1))) A__U61(tt, U42(U43(z0), x1)) -> c26(A__LENGTH(a__U42(a__U43(mark(z0)), x1)), MARK(U42(U43(z0), x1))) A__U61(tt, U42(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatIList(z0), x1)), MARK(U42(isNatIList(z0), x1))) A__U61(tt, U42(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U42(a__U51(mark(z0), z1, z2), x1)), MARK(U42(U51(z0, z1, z2), x1))) A__U61(tt, U42(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U52(mark(z0), z1), x1)), MARK(U42(U52(z0, z1), x1))) A__U61(tt, U42(U53(z0), x1)) -> c26(A__LENGTH(a__U42(a__U53(mark(z0)), x1)), MARK(U42(U53(z0), x1))) A__U61(tt, U42(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U61(mark(z0), z1), x1)), MARK(U42(U61(z0, z1), x1))) A__U61(tt, U42(length(z0), x1)) -> c26(A__LENGTH(a__U42(a__length(mark(z0)), x1)), MARK(U42(length(z0), x1))) A__U61(tt, U42(and(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__and(mark(z0), z1), x1)), MARK(U42(and(z0, z1), x1))) A__U61(tt, U42(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatIListKind(z0), x1)), MARK(U42(isNatIListKind(z0), x1))) A__U61(tt, U42(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatKind(z0), x1)), MARK(U42(isNatKind(z0), x1))) A__U61(tt, U42(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U42(cons(mark(z0), z1), x1)), MARK(U42(cons(z0, z1), x1))) A__U61(tt, U42(tt, x1)) -> c26(A__LENGTH(a__U42(tt, x1)), MARK(U42(tt, x1))) A__U61(tt, U42(s(z0), x1)) -> c26(A__LENGTH(a__U42(s(mark(z0)), x1)), MARK(U42(s(z0), x1))) A__U61(tt, U42(x0, z1)) -> c26(MARK(U42(x0, z1))) A__U61(tt, U42(0, x1)) -> c26(A__LENGTH(a__U42(0, x1))) A__U61(tt, U42(nil, x1)) -> c26(A__LENGTH(a__U42(nil, x1))) A__U61(tt, U43(zeros)) -> c26(A__LENGTH(a__U43(a__zeros)), MARK(U43(zeros))) A__U61(tt, U43(U11(z0, z1))) -> c26(A__LENGTH(a__U43(a__U11(mark(z0), z1))), MARK(U43(U11(z0, z1)))) A__U61(tt, U43(U12(z0))) -> c26(A__LENGTH(a__U43(a__U12(mark(z0)))), MARK(U43(U12(z0)))) A__U61(tt, U43(isNatList(z0))) -> c26(A__LENGTH(a__U43(a__isNatList(z0))), MARK(U43(isNatList(z0)))) A__U61(tt, U43(U21(z0, z1))) -> c26(A__LENGTH(a__U43(a__U21(mark(z0), z1))), MARK(U43(U21(z0, z1)))) A__U61(tt, U43(U22(z0))) -> c26(A__LENGTH(a__U43(a__U22(mark(z0)))), MARK(U43(U22(z0)))) A__U61(tt, U43(isNat(z0))) -> c26(A__LENGTH(a__U43(a__isNat(z0))), MARK(U43(isNat(z0)))) A__U61(tt, U43(U31(z0, z1))) -> c26(A__LENGTH(a__U43(a__U31(mark(z0), z1))), MARK(U43(U31(z0, z1)))) A__U61(tt, U43(U32(z0))) -> c26(A__LENGTH(a__U43(a__U32(mark(z0)))), MARK(U43(U32(z0)))) A__U61(tt, U43(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U43(a__U41(mark(z0), z1, z2))), MARK(U43(U41(z0, z1, z2)))) A__U61(tt, U43(U42(z0, z1))) -> c26(A__LENGTH(a__U43(a__U42(mark(z0), z1))), MARK(U43(U42(z0, z1)))) A__U61(tt, U43(U43(z0))) -> c26(A__LENGTH(a__U43(a__U43(mark(z0)))), MARK(U43(U43(z0)))) A__U61(tt, U43(isNatIList(z0))) -> c26(A__LENGTH(a__U43(a__isNatIList(z0))), MARK(U43(isNatIList(z0)))) A__U61(tt, U43(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U43(a__U51(mark(z0), z1, z2))), MARK(U43(U51(z0, z1, z2)))) A__U61(tt, U43(U52(z0, z1))) -> c26(A__LENGTH(a__U43(a__U52(mark(z0), z1))), MARK(U43(U52(z0, z1)))) A__U61(tt, U43(U53(z0))) -> c26(A__LENGTH(a__U43(a__U53(mark(z0)))), MARK(U43(U53(z0)))) A__U61(tt, U43(U61(z0, z1))) -> c26(A__LENGTH(a__U43(a__U61(mark(z0), z1))), MARK(U43(U61(z0, z1)))) A__U61(tt, U43(length(z0))) -> c26(A__LENGTH(a__U43(a__length(mark(z0)))), MARK(U43(length(z0)))) A__U61(tt, U43(and(z0, z1))) -> c26(A__LENGTH(a__U43(a__and(mark(z0), z1))), MARK(U43(and(z0, z1)))) A__U61(tt, U43(isNatIListKind(z0))) -> c26(A__LENGTH(a__U43(a__isNatIListKind(z0))), MARK(U43(isNatIListKind(z0)))) A__U61(tt, U43(isNatKind(z0))) -> c26(A__LENGTH(a__U43(a__isNatKind(z0))), MARK(U43(isNatKind(z0)))) A__U61(tt, U43(cons(z0, z1))) -> c26(A__LENGTH(a__U43(cons(mark(z0), z1))), MARK(U43(cons(z0, z1)))) A__U61(tt, U43(0)) -> c26(A__LENGTH(a__U43(0)), MARK(U43(0))) A__U61(tt, U43(tt)) -> c26(A__LENGTH(a__U43(tt)), MARK(U43(tt))) A__U61(tt, U43(s(z0))) -> c26(A__LENGTH(a__U43(s(mark(z0)))), MARK(U43(s(z0)))) A__U61(tt, U43(nil)) -> c26(A__LENGTH(a__U43(nil)), MARK(U43(nil))) A__U61(tt, U43(x0)) -> c26(MARK(U43(x0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__U31(a__isNatIListKind(z0), z0)), MARK(isNatIList(z0))) A__U61(tt, isNatIList(cons(z0, z1))) -> c26(A__LENGTH(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatIList(cons(z0, z1)))) A__U61(tt, isNatIList(zeros)) -> c26(MARK(isNatIList(zeros))) A__U61(tt, isNatIList(z0)) -> c26(MARK(isNatIList(z0))) A__U61(tt, U51(zeros, x1, x2)) -> c26(A__LENGTH(a__U51(a__zeros, x1, x2)), MARK(U51(zeros, x1, x2))) A__U61(tt, U51(U11(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U11(mark(z0), z1), x1, x2)), MARK(U51(U11(z0, z1), x1, x2))) A__U61(tt, U51(U12(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U12(mark(z0)), x1, x2)), MARK(U51(U12(z0), x1, x2))) A__U61(tt, U51(isNatList(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatList(z0), x1, x2)), MARK(U51(isNatList(z0), x1, x2))) A__U61(tt, U51(U21(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U21(mark(z0), z1), x1, x2)), MARK(U51(U21(z0, z1), x1, x2))) A__U61(tt, U51(U22(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U22(mark(z0)), x1, x2)), MARK(U51(U22(z0), x1, x2))) A__U61(tt, U51(isNat(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNat(z0), x1, x2)), MARK(U51(isNat(z0), x1, x2))) A__U61(tt, U51(U31(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U31(mark(z0), z1), x1, x2)), MARK(U51(U31(z0, z1), x1, x2))) A__U61(tt, U51(U32(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U32(mark(z0)), x1, x2)), MARK(U51(U32(z0), x1, x2))) A__U61(tt, U51(U41(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U51(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U51(U41(z0, z1, z2), x1, x2))) A__U61(tt, U51(U42(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U42(mark(z0), z1), x1, x2)), MARK(U51(U42(z0, z1), x1, x2))) A__U61(tt, U51(U43(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U43(mark(z0)), x1, x2)), MARK(U51(U43(z0), x1, x2))) A__U61(tt, U51(isNatIList(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatIList(z0), x1, x2)), MARK(U51(isNatIList(z0), x1, x2))) A__U61(tt, U51(U51(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U51(a__U51(mark(z0), z1, z2), x1, x2)), MARK(U51(U51(z0, z1, z2), x1, x2))) A__U61(tt, U51(U52(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U52(mark(z0), z1), x1, x2)), MARK(U51(U52(z0, z1), x1, x2))) A__U61(tt, U51(U53(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U53(mark(z0)), x1, x2)), MARK(U51(U53(z0), x1, x2))) A__U61(tt, U51(U61(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U61(mark(z0), z1), x1, x2)), MARK(U51(U61(z0, z1), x1, x2))) A__U61(tt, U51(length(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__length(mark(z0)), x1, x2)), MARK(U51(length(z0), x1, x2))) A__U61(tt, U51(and(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__and(mark(z0), z1), x1, x2)), MARK(U51(and(z0, z1), x1, x2))) A__U61(tt, U51(isNatIListKind(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatIListKind(z0), x1, x2)), MARK(U51(isNatIListKind(z0), x1, x2))) A__U61(tt, U51(isNatKind(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatKind(z0), x1, x2)), MARK(U51(isNatKind(z0), x1, x2))) A__U61(tt, U51(cons(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(cons(mark(z0), z1), x1, x2)), MARK(U51(cons(z0, z1), x1, x2))) A__U61(tt, U51(tt, x1, x2)) -> c26(A__LENGTH(a__U51(tt, x1, x2)), MARK(U51(tt, x1, x2))) A__U61(tt, U51(s(z0), x1, x2)) -> c26(A__LENGTH(a__U51(s(mark(z0)), x1, x2)), MARK(U51(s(z0), x1, x2))) A__U61(tt, U51(x0, z1, z2)) -> c26(MARK(U51(x0, z1, z2))) A__U61(tt, U51(0, x1, x2)) -> c26(A__LENGTH(a__U51(0, x1, x2))) A__U61(tt, U51(nil, x1, x2)) -> c26(A__LENGTH(a__U51(nil, x1, x2))) A__U61(tt, U52(zeros, x1)) -> c26(A__LENGTH(a__U52(a__zeros, x1)), MARK(U52(zeros, x1))) A__U61(tt, U52(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U11(mark(z0), z1), x1)), MARK(U52(U11(z0, z1), x1))) A__U61(tt, U52(U12(z0), x1)) -> c26(A__LENGTH(a__U52(a__U12(mark(z0)), x1)), MARK(U52(U12(z0), x1))) A__U61(tt, U52(isNatList(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatList(z0), x1)), MARK(U52(isNatList(z0), x1))) A__U61(tt, U52(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U21(mark(z0), z1), x1)), MARK(U52(U21(z0, z1), x1))) A__U61(tt, U52(U22(z0), x1)) -> c26(A__LENGTH(a__U52(a__U22(mark(z0)), x1)), MARK(U52(U22(z0), x1))) A__U61(tt, U52(isNat(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNat(z0), x1)), MARK(U52(isNat(z0), x1))) A__U61(tt, U52(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U31(mark(z0), z1), x1)), MARK(U52(U31(z0, z1), x1))) A__U61(tt, U52(U32(z0), x1)) -> c26(A__LENGTH(a__U52(a__U32(mark(z0)), x1)), MARK(U52(U32(z0), x1))) A__U61(tt, U52(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U52(a__U41(mark(z0), z1, z2), x1)), MARK(U52(U41(z0, z1, z2), x1))) A__U61(tt, U52(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U42(mark(z0), z1), x1)), MARK(U52(U42(z0, z1), x1))) A__U61(tt, U52(U43(z0), x1)) -> c26(A__LENGTH(a__U52(a__U43(mark(z0)), x1)), MARK(U52(U43(z0), x1))) A__U61(tt, U52(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatIList(z0), x1)), MARK(U52(isNatIList(z0), x1))) A__U61(tt, U52(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U52(a__U51(mark(z0), z1, z2), x1)), MARK(U52(U51(z0, z1, z2), x1))) A__U61(tt, U52(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U52(mark(z0), z1), x1)), MARK(U52(U52(z0, z1), x1))) A__U61(tt, U52(U53(z0), x1)) -> c26(A__LENGTH(a__U52(a__U53(mark(z0)), x1)), MARK(U52(U53(z0), x1))) A__U61(tt, U52(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U61(mark(z0), z1), x1)), MARK(U52(U61(z0, z1), x1))) A__U61(tt, U52(length(z0), x1)) -> c26(A__LENGTH(a__U52(a__length(mark(z0)), x1)), MARK(U52(length(z0), x1))) A__U61(tt, U52(and(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__and(mark(z0), z1), x1)), MARK(U52(and(z0, z1), x1))) A__U61(tt, U52(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatIListKind(z0), x1)), MARK(U52(isNatIListKind(z0), x1))) A__U61(tt, U52(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatKind(z0), x1)), MARK(U52(isNatKind(z0), x1))) A__U61(tt, U52(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U52(cons(mark(z0), z1), x1)), MARK(U52(cons(z0, z1), x1))) A__U61(tt, U52(tt, x1)) -> c26(A__LENGTH(a__U52(tt, x1)), MARK(U52(tt, x1))) A__U61(tt, U52(s(z0), x1)) -> c26(A__LENGTH(a__U52(s(mark(z0)), x1)), MARK(U52(s(z0), x1))) A__U61(tt, U52(x0, z1)) -> c26(MARK(U52(x0, z1))) A__U61(tt, U52(0, x1)) -> c26(A__LENGTH(a__U52(0, x1))) A__U61(tt, U52(nil, x1)) -> c26(A__LENGTH(a__U52(nil, x1))) A__U61(tt, U53(x0)) -> c26(A__LENGTH(U53(mark(x0))), MARK(U53(x0))) A__U61(tt, U53(zeros)) -> c26(A__LENGTH(a__U53(a__zeros)), MARK(U53(zeros))) A__U61(tt, U53(U11(z0, z1))) -> c26(A__LENGTH(a__U53(a__U11(mark(z0), z1))), MARK(U53(U11(z0, z1)))) A__U61(tt, U53(U12(z0))) -> c26(A__LENGTH(a__U53(a__U12(mark(z0)))), MARK(U53(U12(z0)))) A__U61(tt, U53(isNatList(z0))) -> c26(A__LENGTH(a__U53(a__isNatList(z0))), MARK(U53(isNatList(z0)))) A__U61(tt, U53(U21(z0, z1))) -> c26(A__LENGTH(a__U53(a__U21(mark(z0), z1))), MARK(U53(U21(z0, z1)))) A__U61(tt, U53(U22(z0))) -> c26(A__LENGTH(a__U53(a__U22(mark(z0)))), MARK(U53(U22(z0)))) A__U61(tt, U53(isNat(z0))) -> c26(A__LENGTH(a__U53(a__isNat(z0))), MARK(U53(isNat(z0)))) A__U61(tt, U53(U31(z0, z1))) -> c26(A__LENGTH(a__U53(a__U31(mark(z0), z1))), MARK(U53(U31(z0, z1)))) A__U61(tt, U53(U32(z0))) -> c26(A__LENGTH(a__U53(a__U32(mark(z0)))), MARK(U53(U32(z0)))) A__U61(tt, U53(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U53(a__U41(mark(z0), z1, z2))), MARK(U53(U41(z0, z1, z2)))) A__U61(tt, U53(U42(z0, z1))) -> c26(A__LENGTH(a__U53(a__U42(mark(z0), z1))), MARK(U53(U42(z0, z1)))) A__U61(tt, U53(U43(z0))) -> c26(A__LENGTH(a__U53(a__U43(mark(z0)))), MARK(U53(U43(z0)))) A__U61(tt, U53(isNatIList(z0))) -> c26(A__LENGTH(a__U53(a__isNatIList(z0))), MARK(U53(isNatIList(z0)))) A__U61(tt, U53(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U53(a__U51(mark(z0), z1, z2))), MARK(U53(U51(z0, z1, z2)))) A__U61(tt, U53(U52(z0, z1))) -> c26(A__LENGTH(a__U53(a__U52(mark(z0), z1))), MARK(U53(U52(z0, z1)))) A__U61(tt, U53(U53(z0))) -> c26(A__LENGTH(a__U53(a__U53(mark(z0)))), MARK(U53(U53(z0)))) A__U61(tt, U53(U61(z0, z1))) -> c26(A__LENGTH(a__U53(a__U61(mark(z0), z1))), MARK(U53(U61(z0, z1)))) A__U61(tt, U53(length(z0))) -> c26(A__LENGTH(a__U53(a__length(mark(z0)))), MARK(U53(length(z0)))) A__U61(tt, U53(and(z0, z1))) -> c26(A__LENGTH(a__U53(a__and(mark(z0), z1))), MARK(U53(and(z0, z1)))) A__U61(tt, U53(isNatIListKind(z0))) -> c26(A__LENGTH(a__U53(a__isNatIListKind(z0))), MARK(U53(isNatIListKind(z0)))) A__U61(tt, U53(isNatKind(z0))) -> c26(A__LENGTH(a__U53(a__isNatKind(z0))), MARK(U53(isNatKind(z0)))) A__U61(tt, U53(cons(z0, z1))) -> c26(A__LENGTH(a__U53(cons(mark(z0), z1))), MARK(U53(cons(z0, z1)))) A__U61(tt, U53(0)) -> c26(A__LENGTH(a__U53(0)), MARK(U53(0))) A__U61(tt, U53(tt)) -> c26(A__LENGTH(a__U53(tt)), MARK(U53(tt))) A__U61(tt, U53(s(z0))) -> c26(A__LENGTH(a__U53(s(mark(z0)))), MARK(U53(s(z0)))) A__U61(tt, U53(nil)) -> c26(A__LENGTH(a__U53(nil)), MARK(U53(nil))) A__U61(tt, U53(x0)) -> c26(MARK(U53(x0))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), 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MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, 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MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, 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MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> 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U51(U61(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U61(mark(z0), z1), x1, x2)), MARK(U51(U61(z0, z1), x1, x2))) A__U61(tt, U51(length(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__length(mark(z0)), x1, x2)), MARK(U51(length(z0), x1, x2))) A__U61(tt, U51(and(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__and(mark(z0), z1), x1, x2)), MARK(U51(and(z0, z1), x1, x2))) A__U61(tt, U51(isNatIListKind(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatIListKind(z0), x1, x2)), MARK(U51(isNatIListKind(z0), x1, x2))) A__U61(tt, U51(isNatKind(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatKind(z0), x1, x2)), MARK(U51(isNatKind(z0), x1, x2))) A__U61(tt, U51(cons(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(cons(mark(z0), z1), x1, x2)), MARK(U51(cons(z0, z1), x1, x2))) A__U61(tt, U51(tt, x1, x2)) -> c26(A__LENGTH(a__U51(tt, x1, x2)), MARK(U51(tt, x1, x2))) A__U61(tt, U51(s(z0), x1, x2)) -> c26(A__LENGTH(a__U51(s(mark(z0)), x1, x2)), MARK(U51(s(z0), x1, x2))) A__U61(tt, U51(x0, z1, z2)) -> c26(MARK(U51(x0, z1, z2))) A__U61(tt, U51(0, x1, x2)) -> c26(A__LENGTH(a__U51(0, x1, x2))) A__U61(tt, U51(nil, x1, x2)) -> c26(A__LENGTH(a__U51(nil, x1, x2))) A__U61(tt, U52(zeros, x1)) -> c26(A__LENGTH(a__U52(a__zeros, x1)), MARK(U52(zeros, x1))) A__U61(tt, U52(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U11(mark(z0), z1), x1)), MARK(U52(U11(z0, z1), x1))) A__U61(tt, U52(U12(z0), x1)) -> c26(A__LENGTH(a__U52(a__U12(mark(z0)), x1)), MARK(U52(U12(z0), x1))) A__U61(tt, U52(isNatList(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatList(z0), x1)), MARK(U52(isNatList(z0), x1))) A__U61(tt, U52(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U21(mark(z0), z1), x1)), MARK(U52(U21(z0, z1), x1))) A__U61(tt, U52(U22(z0), x1)) -> c26(A__LENGTH(a__U52(a__U22(mark(z0)), x1)), MARK(U52(U22(z0), x1))) A__U61(tt, U52(isNat(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNat(z0), x1)), MARK(U52(isNat(z0), x1))) A__U61(tt, U52(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U31(mark(z0), z1), x1)), MARK(U52(U31(z0, z1), x1))) A__U61(tt, U52(U32(z0), x1)) -> c26(A__LENGTH(a__U52(a__U32(mark(z0)), x1)), MARK(U52(U32(z0), x1))) A__U61(tt, U52(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U52(a__U41(mark(z0), z1, z2), x1)), MARK(U52(U41(z0, z1, z2), x1))) A__U61(tt, U52(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U42(mark(z0), z1), x1)), MARK(U52(U42(z0, z1), x1))) A__U61(tt, U52(U43(z0), x1)) -> c26(A__LENGTH(a__U52(a__U43(mark(z0)), x1)), MARK(U52(U43(z0), x1))) A__U61(tt, U52(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatIList(z0), x1)), MARK(U52(isNatIList(z0), x1))) A__U61(tt, U52(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U52(a__U51(mark(z0), z1, z2), x1)), MARK(U52(U51(z0, z1, z2), x1))) A__U61(tt, U52(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U52(mark(z0), z1), x1)), MARK(U52(U52(z0, z1), x1))) A__U61(tt, U52(U53(z0), x1)) -> c26(A__LENGTH(a__U52(a__U53(mark(z0)), x1)), MARK(U52(U53(z0), x1))) A__U61(tt, U52(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U61(mark(z0), z1), x1)), MARK(U52(U61(z0, z1), x1))) A__U61(tt, U52(length(z0), x1)) -> c26(A__LENGTH(a__U52(a__length(mark(z0)), x1)), MARK(U52(length(z0), x1))) A__U61(tt, U52(and(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__and(mark(z0), z1), x1)), MARK(U52(and(z0, z1), x1))) A__U61(tt, U52(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatIListKind(z0), x1)), MARK(U52(isNatIListKind(z0), x1))) A__U61(tt, U52(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatKind(z0), x1)), MARK(U52(isNatKind(z0), x1))) A__U61(tt, U52(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U52(cons(mark(z0), z1), x1)), MARK(U52(cons(z0, z1), x1))) A__U61(tt, U52(tt, x1)) -> c26(A__LENGTH(a__U52(tt, x1)), MARK(U52(tt, x1))) A__U61(tt, U52(s(z0), x1)) -> c26(A__LENGTH(a__U52(s(mark(z0)), x1)), MARK(U52(s(z0), x1))) A__U61(tt, U52(x0, z1)) -> c26(MARK(U52(x0, z1))) A__U61(tt, U52(0, x1)) -> c26(A__LENGTH(a__U52(0, x1))) A__U61(tt, U52(nil, x1)) -> c26(A__LENGTH(a__U52(nil, x1))) A__U61(tt, U53(x0)) -> c26(A__LENGTH(U53(mark(x0))), MARK(U53(x0))) A__U61(tt, U53(zeros)) -> c26(A__LENGTH(a__U53(a__zeros)), MARK(U53(zeros))) A__U61(tt, U53(U11(z0, z1))) -> c26(A__LENGTH(a__U53(a__U11(mark(z0), z1))), MARK(U53(U11(z0, z1)))) A__U61(tt, U53(U12(z0))) -> c26(A__LENGTH(a__U53(a__U12(mark(z0)))), MARK(U53(U12(z0)))) A__U61(tt, U53(isNatList(z0))) -> c26(A__LENGTH(a__U53(a__isNatList(z0))), MARK(U53(isNatList(z0)))) A__U61(tt, U53(U21(z0, z1))) -> c26(A__LENGTH(a__U53(a__U21(mark(z0), z1))), MARK(U53(U21(z0, z1)))) A__U61(tt, U53(U22(z0))) -> c26(A__LENGTH(a__U53(a__U22(mark(z0)))), MARK(U53(U22(z0)))) A__U61(tt, U53(isNat(z0))) -> c26(A__LENGTH(a__U53(a__isNat(z0))), MARK(U53(isNat(z0)))) A__U61(tt, U53(U31(z0, z1))) -> c26(A__LENGTH(a__U53(a__U31(mark(z0), z1))), MARK(U53(U31(z0, z1)))) A__U61(tt, U53(U32(z0))) -> c26(A__LENGTH(a__U53(a__U32(mark(z0)))), MARK(U53(U32(z0)))) A__U61(tt, U53(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U53(a__U41(mark(z0), z1, z2))), MARK(U53(U41(z0, z1, z2)))) A__U61(tt, U53(U42(z0, z1))) -> c26(A__LENGTH(a__U53(a__U42(mark(z0), z1))), MARK(U53(U42(z0, z1)))) A__U61(tt, U53(U43(z0))) -> c26(A__LENGTH(a__U53(a__U43(mark(z0)))), MARK(U53(U43(z0)))) A__U61(tt, U53(isNatIList(z0))) -> c26(A__LENGTH(a__U53(a__isNatIList(z0))), MARK(U53(isNatIList(z0)))) A__U61(tt, U53(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U53(a__U51(mark(z0), z1, z2))), MARK(U53(U51(z0, z1, z2)))) A__U61(tt, U53(U52(z0, z1))) -> c26(A__LENGTH(a__U53(a__U52(mark(z0), z1))), MARK(U53(U52(z0, z1)))) A__U61(tt, U53(U53(z0))) -> c26(A__LENGTH(a__U53(a__U53(mark(z0)))), MARK(U53(U53(z0)))) A__U61(tt, U53(U61(z0, z1))) -> c26(A__LENGTH(a__U53(a__U61(mark(z0), z1))), MARK(U53(U61(z0, z1)))) A__U61(tt, U53(length(z0))) -> c26(A__LENGTH(a__U53(a__length(mark(z0)))), MARK(U53(length(z0)))) A__U61(tt, U53(and(z0, z1))) -> c26(A__LENGTH(a__U53(a__and(mark(z0), z1))), MARK(U53(and(z0, z1)))) A__U61(tt, U53(isNatIListKind(z0))) -> c26(A__LENGTH(a__U53(a__isNatIListKind(z0))), MARK(U53(isNatIListKind(z0)))) A__U61(tt, U53(isNatKind(z0))) -> c26(A__LENGTH(a__U53(a__isNatKind(z0))), MARK(U53(isNatKind(z0)))) A__U61(tt, U53(cons(z0, z1))) -> c26(A__LENGTH(a__U53(cons(mark(z0), z1))), MARK(U53(cons(z0, z1)))) A__U61(tt, U53(0)) -> c26(A__LENGTH(a__U53(0)), MARK(U53(0))) A__U61(tt, U53(tt)) -> c26(A__LENGTH(a__U53(tt)), MARK(U53(tt))) A__U61(tt, U53(s(z0))) -> c26(A__LENGTH(a__U53(s(mark(z0)))), MARK(U53(s(z0)))) A__U61(tt, U53(nil)) -> c26(A__LENGTH(a__U53(nil)), MARK(U53(nil))) A__U61(tt, U53(x0)) -> c26(MARK(U53(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_1, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c14_2, c20_2 ---------------------------------------- (205) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> c26(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U61(tt, U12(U21(z0, z1))) -> c26(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U61(tt, U12(U22(z0))) -> c26(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U61(tt, U12(isNat(z0))) -> c26(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U61(tt, U12(U31(z0, z1))) -> c26(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U61(tt, U12(U32(z0))) -> c26(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U61(tt, U12(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U61(tt, U12(U42(z0, z1))) -> c26(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U61(tt, U12(U43(z0))) -> c26(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U61(tt, U12(isNatIList(z0))) -> c26(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U61(tt, U12(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U61(tt, U12(U52(z0, z1))) -> c26(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U61(tt, U12(U53(z0))) -> c26(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U61(tt, U12(U61(z0, z1))) -> c26(A__LENGTH(a__U12(a__U61(mark(z0), z1))), MARK(U12(U61(z0, z1)))) A__U61(tt, U12(length(z0))) -> c26(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U61(tt, U12(and(z0, z1))) -> c26(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U61(tt, U12(isNatIListKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U61(tt, U12(isNatKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U61(tt, U12(cons(z0, z1))) -> c26(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U61(tt, U12(0)) -> c26(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U61(tt, U12(tt)) -> c26(A__LENGTH(a__U12(tt)), MARK(U12(tt))) A__U61(tt, U12(s(z0))) -> c26(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U61(tt, U12(nil)) -> c26(A__LENGTH(a__U12(nil)), MARK(U12(nil))) A__U61(tt, U12(x0)) -> c26(MARK(U12(x0))) A__U61(tt, isNatList(cons(z0, z1))) -> c26(A__LENGTH(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(cons(z0, z1)))) A__U61(tt, isNatList(nil)) -> c26(MARK(isNatList(nil))) A__U61(tt, isNatList(z0)) -> c26(MARK(isNatList(z0))) A__U61(tt, U21(zeros, x1)) -> c26(A__LENGTH(a__U21(a__zeros, x1)), MARK(U21(zeros, x1))) A__U61(tt, U21(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1)), MARK(U21(U11(z0, z1), x1))) A__U61(tt, U21(U12(z0), x1)) -> c26(A__LENGTH(a__U21(a__U12(mark(z0)), x1)), MARK(U21(U12(z0), x1))) A__U61(tt, U21(isNatList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatList(z0), x1)), MARK(U21(isNatList(z0), x1))) A__U61(tt, U21(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U21(mark(z0), z1), x1)), MARK(U21(U21(z0, z1), x1))) A__U61(tt, U21(U22(z0), x1)) -> c26(A__LENGTH(a__U21(a__U22(mark(z0)), x1)), MARK(U21(U22(z0), x1))) A__U61(tt, U21(isNat(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNat(z0), x1)), MARK(U21(isNat(z0), x1))) A__U61(tt, U21(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U31(mark(z0), z1), x1)), MARK(U21(U31(z0, z1), x1))) A__U61(tt, U21(U32(z0), x1)) -> c26(A__LENGTH(a__U21(a__U32(mark(z0)), x1)), MARK(U21(U32(z0), x1))) A__U61(tt, U21(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(U21(U41(z0, z1, z2), x1))) A__U61(tt, U21(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U42(mark(z0), z1), x1)), MARK(U21(U42(z0, z1), x1))) A__U61(tt, U21(U43(z0), x1)) -> c26(A__LENGTH(a__U21(a__U43(mark(z0)), x1)), MARK(U21(U43(z0), x1))) A__U61(tt, U21(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIList(z0), x1)), MARK(U21(isNatIList(z0), x1))) A__U61(tt, U21(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U51(mark(z0), z1, z2), x1)), MARK(U21(U51(z0, z1, z2), x1))) A__U61(tt, U21(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U52(mark(z0), z1), x1)), MARK(U21(U52(z0, z1), x1))) A__U61(tt, U21(U53(z0), x1)) -> c26(A__LENGTH(a__U21(a__U53(mark(z0)), x1)), MARK(U21(U53(z0), x1))) A__U61(tt, U21(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U61(mark(z0), z1), x1)), MARK(U21(U61(z0, z1), x1))) A__U61(tt, U21(length(z0), x1)) -> c26(A__LENGTH(a__U21(a__length(mark(z0)), x1)), MARK(U21(length(z0), x1))) A__U61(tt, U21(and(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__and(mark(z0), z1), x1)), MARK(U21(and(z0, z1), x1))) A__U61(tt, U21(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIListKind(z0), x1)), MARK(U21(isNatIListKind(z0), x1))) A__U61(tt, U21(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), x1)), MARK(U21(isNatKind(z0), x1))) A__U61(tt, U21(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U21(cons(mark(z0), z1), x1)), MARK(U21(cons(z0, z1), x1))) A__U61(tt, U21(tt, x1)) -> c26(A__LENGTH(a__U21(tt, x1)), MARK(U21(tt, x1))) A__U61(tt, U21(s(z0), x1)) -> c26(A__LENGTH(a__U21(s(mark(z0)), x1)), MARK(U21(s(z0), x1))) A__U61(tt, U21(x0, z1)) -> c26(MARK(U21(x0, z1))) A__U61(tt, U21(0, x1)) -> c26(A__LENGTH(a__U21(0, x1))) A__U61(tt, U21(nil, x1)) -> c26(A__LENGTH(a__U21(nil, x1))) A__U61(tt, U22(zeros)) -> c26(A__LENGTH(a__U22(a__zeros)), MARK(U22(zeros))) A__U61(tt, U22(U11(z0, z1))) -> c26(A__LENGTH(a__U22(a__U11(mark(z0), z1))), MARK(U22(U11(z0, z1)))) A__U61(tt, U22(U12(z0))) -> c26(A__LENGTH(a__U22(a__U12(mark(z0)))), MARK(U22(U12(z0)))) A__U61(tt, U22(isNatList(z0))) -> c26(A__LENGTH(a__U22(a__isNatList(z0))), MARK(U22(isNatList(z0)))) A__U61(tt, U22(U21(z0, z1))) -> c26(A__LENGTH(a__U22(a__U21(mark(z0), z1))), MARK(U22(U21(z0, z1)))) A__U61(tt, U22(U22(z0))) -> c26(A__LENGTH(a__U22(a__U22(mark(z0)))), MARK(U22(U22(z0)))) A__U61(tt, U22(isNat(z0))) -> c26(A__LENGTH(a__U22(a__isNat(z0))), MARK(U22(isNat(z0)))) A__U61(tt, U22(U31(z0, z1))) -> c26(A__LENGTH(a__U22(a__U31(mark(z0), z1))), MARK(U22(U31(z0, z1)))) A__U61(tt, U22(U32(z0))) -> c26(A__LENGTH(a__U22(a__U32(mark(z0)))), MARK(U22(U32(z0)))) A__U61(tt, U22(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U22(a__U41(mark(z0), z1, z2))), MARK(U22(U41(z0, z1, z2)))) A__U61(tt, U22(U42(z0, z1))) -> c26(A__LENGTH(a__U22(a__U42(mark(z0), z1))), MARK(U22(U42(z0, z1)))) A__U61(tt, U22(U43(z0))) -> c26(A__LENGTH(a__U22(a__U43(mark(z0)))), MARK(U22(U43(z0)))) A__U61(tt, U22(isNatIList(z0))) -> c26(A__LENGTH(a__U22(a__isNatIList(z0))), MARK(U22(isNatIList(z0)))) A__U61(tt, U22(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U22(a__U51(mark(z0), z1, z2))), MARK(U22(U51(z0, z1, z2)))) A__U61(tt, U22(U52(z0, z1))) -> c26(A__LENGTH(a__U22(a__U52(mark(z0), z1))), MARK(U22(U52(z0, z1)))) A__U61(tt, U22(U53(z0))) -> c26(A__LENGTH(a__U22(a__U53(mark(z0)))), MARK(U22(U53(z0)))) A__U61(tt, U22(U61(z0, z1))) -> c26(A__LENGTH(a__U22(a__U61(mark(z0), z1))), MARK(U22(U61(z0, z1)))) A__U61(tt, U22(length(z0))) -> c26(A__LENGTH(a__U22(a__length(mark(z0)))), MARK(U22(length(z0)))) A__U61(tt, U22(and(z0, z1))) -> c26(A__LENGTH(a__U22(a__and(mark(z0), z1))), MARK(U22(and(z0, z1)))) A__U61(tt, U22(isNatIListKind(z0))) -> c26(A__LENGTH(a__U22(a__isNatIListKind(z0))), MARK(U22(isNatIListKind(z0)))) A__U61(tt, U22(isNatKind(z0))) -> c26(A__LENGTH(a__U22(a__isNatKind(z0))), MARK(U22(isNatKind(z0)))) A__U61(tt, U22(cons(z0, z1))) -> c26(A__LENGTH(a__U22(cons(mark(z0), z1))), MARK(U22(cons(z0, z1)))) A__U61(tt, 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MARK(U31(isNatList(z0), x1))) A__U61(tt, U31(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U21(mark(z0), z1), x1)), MARK(U31(U21(z0, z1), x1))) A__U61(tt, U31(U22(z0), x1)) -> c26(A__LENGTH(a__U31(a__U22(mark(z0)), x1)), MARK(U31(U22(z0), x1))) A__U61(tt, U31(isNat(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNat(z0), x1)), MARK(U31(isNat(z0), x1))) A__U61(tt, U31(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U31(mark(z0), z1), x1)), MARK(U31(U31(z0, z1), x1))) A__U61(tt, U31(U32(z0), x1)) -> c26(A__LENGTH(a__U31(a__U32(mark(z0)), x1)), MARK(U31(U32(z0), x1))) A__U61(tt, U31(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(U31(U41(z0, z1, z2), x1))) A__U61(tt, U31(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U31(a__U42(mark(z0), z1), x1)), MARK(U31(U42(z0, z1), x1))) A__U61(tt, U31(U43(z0), x1)) -> c26(A__LENGTH(a__U31(a__U43(mark(z0)), x1)), MARK(U31(U43(z0), x1))) A__U61(tt, U31(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U31(a__isNatIList(z0), x1)), 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-> c26(A__LENGTH(a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2))) A__U61(tt, U41(U42(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U42(mark(z0), z1), x1, x2)), MARK(U41(U42(z0, z1), x1, x2))) A__U61(tt, U41(U43(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U43(mark(z0)), x1, x2)), MARK(U41(U43(z0), x1, x2))) A__U61(tt, U41(isNatIList(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatIList(z0), x1, x2)), MARK(U41(isNatIList(z0), x1, x2))) A__U61(tt, U41(U51(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U41(a__U51(mark(z0), z1, z2), x1, x2)), MARK(U41(U51(z0, z1, z2), x1, x2))) A__U61(tt, U41(U52(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U52(mark(z0), z1), x1, x2)), MARK(U41(U52(z0, z1), x1, x2))) A__U61(tt, U41(U53(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U53(mark(z0)), x1, x2)), MARK(U41(U53(z0), x1, x2))) A__U61(tt, U41(U61(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U61(mark(z0), z1), x1, x2)), MARK(U41(U61(z0, z1), x1, x2))) A__U61(tt, U41(length(z0), x1, x2)) -> 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U43(0)) -> c26(A__LENGTH(a__U43(0)), MARK(U43(0))) A__U61(tt, U43(tt)) -> c26(A__LENGTH(a__U43(tt)), MARK(U43(tt))) A__U61(tt, U43(s(z0))) -> c26(A__LENGTH(a__U43(s(mark(z0)))), MARK(U43(s(z0)))) A__U61(tt, U43(nil)) -> c26(A__LENGTH(a__U43(nil)), MARK(U43(nil))) A__U61(tt, U43(x0)) -> c26(MARK(U43(x0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__U31(a__isNatIListKind(z0), z0)), MARK(isNatIList(z0))) A__U61(tt, isNatIList(cons(z0, z1))) -> c26(A__LENGTH(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatIList(cons(z0, z1)))) A__U61(tt, isNatIList(zeros)) -> c26(MARK(isNatIList(zeros))) A__U61(tt, isNatIList(z0)) -> c26(MARK(isNatIList(z0))) A__U61(tt, U51(zeros, x1, x2)) -> c26(A__LENGTH(a__U51(a__zeros, x1, x2)), MARK(U51(zeros, x1, x2))) A__U61(tt, U51(U11(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U11(mark(z0), z1), x1, x2)), MARK(U51(U11(z0, z1), x1, x2))) A__U61(tt, U51(U12(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U12(mark(z0)), x1, x2)), MARK(U51(U12(z0), x1, x2))) A__U61(tt, U51(isNatList(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatList(z0), x1, x2)), MARK(U51(isNatList(z0), x1, x2))) A__U61(tt, U51(U21(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U21(mark(z0), z1), x1, x2)), MARK(U51(U21(z0, z1), x1, x2))) A__U61(tt, U51(U22(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U22(mark(z0)), x1, x2)), MARK(U51(U22(z0), x1, x2))) A__U61(tt, U51(isNat(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNat(z0), x1, x2)), MARK(U51(isNat(z0), x1, x2))) A__U61(tt, U51(U31(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U31(mark(z0), z1), x1, x2)), MARK(U51(U31(z0, z1), x1, x2))) A__U61(tt, U51(U32(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U32(mark(z0)), x1, x2)), MARK(U51(U32(z0), x1, x2))) A__U61(tt, U51(U41(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U51(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U51(U41(z0, z1, z2), x1, x2))) A__U61(tt, U51(U42(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U42(mark(z0), z1), x1, x2)), MARK(U51(U42(z0, z1), x1, x2))) A__U61(tt, U51(U43(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U43(mark(z0)), x1, x2)), MARK(U51(U43(z0), x1, x2))) A__U61(tt, U51(isNatIList(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatIList(z0), x1, x2)), MARK(U51(isNatIList(z0), x1, x2))) A__U61(tt, U51(U51(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U51(a__U51(mark(z0), z1, z2), x1, x2)), MARK(U51(U51(z0, z1, z2), x1, x2))) A__U61(tt, U51(U52(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U52(mark(z0), z1), x1, x2)), MARK(U51(U52(z0, z1), x1, x2))) A__U61(tt, U51(U53(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U53(mark(z0)), x1, x2)), MARK(U51(U53(z0), x1, x2))) A__U61(tt, U51(U61(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U61(mark(z0), z1), x1, x2)), MARK(U51(U61(z0, z1), x1, x2))) A__U61(tt, U51(length(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__length(mark(z0)), x1, x2)), MARK(U51(length(z0), x1, x2))) A__U61(tt, U51(and(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__and(mark(z0), z1), x1, x2)), MARK(U51(and(z0, z1), x1, x2))) A__U61(tt, U51(isNatIListKind(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatIListKind(z0), x1, x2)), MARK(U51(isNatIListKind(z0), x1, x2))) A__U61(tt, U51(isNatKind(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatKind(z0), x1, x2)), MARK(U51(isNatKind(z0), x1, x2))) A__U61(tt, U51(cons(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(cons(mark(z0), z1), x1, x2)), MARK(U51(cons(z0, z1), x1, x2))) A__U61(tt, U51(tt, x1, x2)) -> c26(A__LENGTH(a__U51(tt, x1, x2)), MARK(U51(tt, x1, x2))) A__U61(tt, U51(s(z0), x1, x2)) -> c26(A__LENGTH(a__U51(s(mark(z0)), x1, x2)), MARK(U51(s(z0), x1, x2))) A__U61(tt, U51(x0, z1, z2)) -> c26(MARK(U51(x0, z1, z2))) A__U61(tt, U51(0, x1, x2)) -> c26(A__LENGTH(a__U51(0, x1, x2))) A__U61(tt, U51(nil, x1, x2)) -> c26(A__LENGTH(a__U51(nil, x1, x2))) A__U61(tt, U52(zeros, x1)) -> c26(A__LENGTH(a__U52(a__zeros, x1)), MARK(U52(zeros, x1))) A__U61(tt, U52(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U11(mark(z0), z1), x1)), MARK(U52(U11(z0, z1), x1))) A__U61(tt, U52(U12(z0), x1)) -> c26(A__LENGTH(a__U52(a__U12(mark(z0)), x1)), MARK(U52(U12(z0), x1))) A__U61(tt, U52(isNatList(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatList(z0), x1)), MARK(U52(isNatList(z0), x1))) A__U61(tt, U52(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U21(mark(z0), z1), x1)), MARK(U52(U21(z0, z1), x1))) A__U61(tt, U52(U22(z0), x1)) -> c26(A__LENGTH(a__U52(a__U22(mark(z0)), x1)), MARK(U52(U22(z0), x1))) A__U61(tt, U52(isNat(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNat(z0), x1)), MARK(U52(isNat(z0), x1))) A__U61(tt, U52(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U31(mark(z0), z1), x1)), MARK(U52(U31(z0, z1), x1))) A__U61(tt, U52(U32(z0), x1)) -> c26(A__LENGTH(a__U52(a__U32(mark(z0)), x1)), MARK(U52(U32(z0), x1))) A__U61(tt, U52(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U52(a__U41(mark(z0), z1, z2), x1)), MARK(U52(U41(z0, z1, z2), x1))) A__U61(tt, U52(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U42(mark(z0), z1), x1)), MARK(U52(U42(z0, z1), x1))) A__U61(tt, U52(U43(z0), x1)) -> c26(A__LENGTH(a__U52(a__U43(mark(z0)), x1)), MARK(U52(U43(z0), x1))) A__U61(tt, U52(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatIList(z0), x1)), MARK(U52(isNatIList(z0), x1))) A__U61(tt, U52(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U52(a__U51(mark(z0), z1, z2), x1)), MARK(U52(U51(z0, z1, z2), x1))) A__U61(tt, U52(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U52(mark(z0), z1), x1)), MARK(U52(U52(z0, z1), x1))) A__U61(tt, U52(U53(z0), x1)) -> c26(A__LENGTH(a__U52(a__U53(mark(z0)), x1)), MARK(U52(U53(z0), x1))) A__U61(tt, U52(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U61(mark(z0), z1), x1)), MARK(U52(U61(z0, z1), x1))) A__U61(tt, U52(length(z0), x1)) -> c26(A__LENGTH(a__U52(a__length(mark(z0)), x1)), MARK(U52(length(z0), x1))) A__U61(tt, U52(and(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__and(mark(z0), z1), x1)), MARK(U52(and(z0, z1), x1))) A__U61(tt, U52(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatIListKind(z0), x1)), MARK(U52(isNatIListKind(z0), x1))) A__U61(tt, U52(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatKind(z0), x1)), MARK(U52(isNatKind(z0), x1))) A__U61(tt, U52(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U52(cons(mark(z0), z1), x1)), MARK(U52(cons(z0, z1), x1))) A__U61(tt, U52(tt, x1)) -> c26(A__LENGTH(a__U52(tt, x1)), MARK(U52(tt, x1))) A__U61(tt, U52(s(z0), x1)) -> c26(A__LENGTH(a__U52(s(mark(z0)), x1)), MARK(U52(s(z0), x1))) A__U61(tt, U52(x0, z1)) -> c26(MARK(U52(x0, z1))) A__U61(tt, U52(0, x1)) -> c26(A__LENGTH(a__U52(0, x1))) A__U61(tt, U52(nil, x1)) -> c26(A__LENGTH(a__U52(nil, x1))) A__U61(tt, U53(zeros)) -> c26(A__LENGTH(a__U53(a__zeros)), MARK(U53(zeros))) A__U61(tt, U53(U11(z0, z1))) -> c26(A__LENGTH(a__U53(a__U11(mark(z0), z1))), MARK(U53(U11(z0, z1)))) A__U61(tt, U53(U12(z0))) -> c26(A__LENGTH(a__U53(a__U12(mark(z0)))), MARK(U53(U12(z0)))) A__U61(tt, U53(isNatList(z0))) -> c26(A__LENGTH(a__U53(a__isNatList(z0))), MARK(U53(isNatList(z0)))) A__U61(tt, U53(U21(z0, z1))) -> c26(A__LENGTH(a__U53(a__U21(mark(z0), z1))), MARK(U53(U21(z0, z1)))) A__U61(tt, U53(U22(z0))) -> c26(A__LENGTH(a__U53(a__U22(mark(z0)))), MARK(U53(U22(z0)))) A__U61(tt, U53(isNat(z0))) -> c26(A__LENGTH(a__U53(a__isNat(z0))), MARK(U53(isNat(z0)))) A__U61(tt, U53(U31(z0, z1))) -> c26(A__LENGTH(a__U53(a__U31(mark(z0), z1))), MARK(U53(U31(z0, z1)))) A__U61(tt, U53(U32(z0))) -> c26(A__LENGTH(a__U53(a__U32(mark(z0)))), MARK(U53(U32(z0)))) A__U61(tt, U53(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U53(a__U41(mark(z0), z1, z2))), MARK(U53(U41(z0, z1, z2)))) A__U61(tt, U53(U42(z0, z1))) -> c26(A__LENGTH(a__U53(a__U42(mark(z0), z1))), MARK(U53(U42(z0, z1)))) A__U61(tt, U53(U43(z0))) -> c26(A__LENGTH(a__U53(a__U43(mark(z0)))), MARK(U53(U43(z0)))) A__U61(tt, U53(isNatIList(z0))) -> c26(A__LENGTH(a__U53(a__isNatIList(z0))), MARK(U53(isNatIList(z0)))) A__U61(tt, U53(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U53(a__U51(mark(z0), z1, z2))), MARK(U53(U51(z0, z1, z2)))) A__U61(tt, U53(U52(z0, z1))) -> c26(A__LENGTH(a__U53(a__U52(mark(z0), z1))), MARK(U53(U52(z0, z1)))) A__U61(tt, U53(U53(z0))) -> c26(A__LENGTH(a__U53(a__U53(mark(z0)))), MARK(U53(U53(z0)))) A__U61(tt, U53(U61(z0, z1))) -> c26(A__LENGTH(a__U53(a__U61(mark(z0), z1))), MARK(U53(U61(z0, z1)))) A__U61(tt, U53(length(z0))) -> c26(A__LENGTH(a__U53(a__length(mark(z0)))), MARK(U53(length(z0)))) A__U61(tt, U53(and(z0, z1))) -> c26(A__LENGTH(a__U53(a__and(mark(z0), z1))), MARK(U53(and(z0, z1)))) A__U61(tt, U53(isNatIListKind(z0))) -> c26(A__LENGTH(a__U53(a__isNatIListKind(z0))), MARK(U53(isNatIListKind(z0)))) A__U61(tt, U53(isNatKind(z0))) -> c26(A__LENGTH(a__U53(a__isNatKind(z0))), MARK(U53(isNatKind(z0)))) A__U61(tt, U53(cons(z0, z1))) -> c26(A__LENGTH(a__U53(cons(mark(z0), z1))), MARK(U53(cons(z0, z1)))) A__U61(tt, U53(0)) -> c26(A__LENGTH(a__U53(0)), MARK(U53(0))) A__U61(tt, U53(tt)) -> c26(A__LENGTH(a__U53(tt)), MARK(U53(tt))) A__U61(tt, U53(s(z0))) -> c26(A__LENGTH(a__U53(s(mark(z0)))), MARK(U53(s(z0)))) A__U61(tt, U53(nil)) -> c26(A__LENGTH(a__U53(nil)), MARK(U53(nil))) A__U61(tt, U53(x0)) -> c26(MARK(U53(x0))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U61(tt, length(z0)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> c26(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U61(tt, U12(U21(z0, z1))) -> c26(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U61(tt, U12(U22(z0))) -> c26(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U61(tt, U12(isNat(z0))) -> c26(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U61(tt, U12(U31(z0, z1))) -> c26(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U61(tt, U12(U32(z0))) -> c26(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U61(tt, U12(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U61(tt, U12(U42(z0, z1))) -> c26(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U61(tt, U12(U43(z0))) -> c26(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U61(tt, U12(isNatIList(z0))) -> c26(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U61(tt, U12(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U61(tt, U12(U52(z0, z1))) -> c26(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U61(tt, U12(U53(z0))) -> c26(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U61(tt, U12(U61(z0, z1))) -> c26(A__LENGTH(a__U12(a__U61(mark(z0), z1))), MARK(U12(U61(z0, z1)))) A__U61(tt, U12(length(z0))) -> c26(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U61(tt, U12(and(z0, z1))) -> c26(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U61(tt, U12(isNatIListKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U61(tt, U12(isNatKind(z0))) -> c26(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U61(tt, U12(cons(z0, z1))) -> c26(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U61(tt, U12(0)) -> c26(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U61(tt, U12(tt)) -> c26(A__LENGTH(a__U12(tt)), MARK(U12(tt))) A__U61(tt, U12(s(z0))) -> c26(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U61(tt, U12(nil)) -> c26(A__LENGTH(a__U12(nil)), MARK(U12(nil))) A__U61(tt, U12(x0)) -> c26(MARK(U12(x0))) A__U61(tt, isNatList(cons(z0, z1))) -> c26(A__LENGTH(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(cons(z0, z1)))) A__U61(tt, isNatList(nil)) -> c26(MARK(isNatList(nil))) A__U61(tt, isNatList(z0)) -> c26(MARK(isNatList(z0))) A__U61(tt, U21(zeros, x1)) -> c26(A__LENGTH(a__U21(a__zeros, x1)), MARK(U21(zeros, x1))) A__U61(tt, U21(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1)), MARK(U21(U11(z0, z1), x1))) A__U61(tt, U21(U12(z0), x1)) -> c26(A__LENGTH(a__U21(a__U12(mark(z0)), x1)), MARK(U21(U12(z0), x1))) A__U61(tt, U21(isNatList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatList(z0), x1)), MARK(U21(isNatList(z0), x1))) A__U61(tt, U21(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U21(mark(z0), z1), x1)), MARK(U21(U21(z0, z1), x1))) A__U61(tt, U21(U22(z0), x1)) -> c26(A__LENGTH(a__U21(a__U22(mark(z0)), x1)), MARK(U21(U22(z0), x1))) A__U61(tt, U21(isNat(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNat(z0), x1)), MARK(U21(isNat(z0), x1))) A__U61(tt, U21(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U31(mark(z0), z1), x1)), MARK(U21(U31(z0, z1), x1))) A__U61(tt, U21(U32(z0), x1)) -> c26(A__LENGTH(a__U21(a__U32(mark(z0)), x1)), MARK(U21(U32(z0), x1))) A__U61(tt, U21(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(U21(U41(z0, z1, z2), x1))) A__U61(tt, U21(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U42(mark(z0), z1), x1)), MARK(U21(U42(z0, z1), x1))) A__U61(tt, U21(U43(z0), x1)) -> c26(A__LENGTH(a__U21(a__U43(mark(z0)), x1)), MARK(U21(U43(z0), x1))) A__U61(tt, U21(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIList(z0), x1)), MARK(U21(isNatIList(z0), x1))) A__U61(tt, U21(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U21(a__U51(mark(z0), z1, z2), x1)), MARK(U21(U51(z0, z1, z2), x1))) A__U61(tt, U21(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U52(mark(z0), z1), x1)), MARK(U21(U52(z0, z1), x1))) A__U61(tt, U21(U53(z0), x1)) -> c26(A__LENGTH(a__U21(a__U53(mark(z0)), x1)), MARK(U21(U53(z0), x1))) A__U61(tt, U21(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__U61(mark(z0), z1), x1)), MARK(U21(U61(z0, z1), x1))) A__U61(tt, U21(length(z0), x1)) -> c26(A__LENGTH(a__U21(a__length(mark(z0)), x1)), MARK(U21(length(z0), x1))) A__U61(tt, U21(and(z0, z1), x1)) -> c26(A__LENGTH(a__U21(a__and(mark(z0), z1), x1)), MARK(U21(and(z0, z1), x1))) A__U61(tt, U21(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatIListKind(z0), x1)), MARK(U21(isNatIListKind(z0), x1))) A__U61(tt, U21(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U21(a__isNatKind(z0), x1)), MARK(U21(isNatKind(z0), x1))) A__U61(tt, U21(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U21(cons(mark(z0), z1), x1)), MARK(U21(cons(z0, z1), x1))) A__U61(tt, U21(tt, x1)) -> c26(A__LENGTH(a__U21(tt, x1)), MARK(U21(tt, x1))) A__U61(tt, U21(s(z0), x1)) -> c26(A__LENGTH(a__U21(s(mark(z0)), x1)), MARK(U21(s(z0), x1))) A__U61(tt, U21(x0, z1)) -> c26(MARK(U21(x0, z1))) A__U61(tt, U21(0, x1)) -> c26(A__LENGTH(a__U21(0, x1))) A__U61(tt, U21(nil, x1)) -> c26(A__LENGTH(a__U21(nil, x1))) A__U61(tt, U22(zeros)) -> c26(A__LENGTH(a__U22(a__zeros)), MARK(U22(zeros))) A__U61(tt, U22(U11(z0, z1))) -> c26(A__LENGTH(a__U22(a__U11(mark(z0), z1))), MARK(U22(U11(z0, z1)))) A__U61(tt, U22(U12(z0))) -> c26(A__LENGTH(a__U22(a__U12(mark(z0)))), MARK(U22(U12(z0)))) A__U61(tt, U22(isNatList(z0))) -> c26(A__LENGTH(a__U22(a__isNatList(z0))), MARK(U22(isNatList(z0)))) A__U61(tt, U22(U21(z0, z1))) -> c26(A__LENGTH(a__U22(a__U21(mark(z0), z1))), MARK(U22(U21(z0, z1)))) A__U61(tt, U22(U22(z0))) -> c26(A__LENGTH(a__U22(a__U22(mark(z0)))), MARK(U22(U22(z0)))) A__U61(tt, U22(isNat(z0))) -> c26(A__LENGTH(a__U22(a__isNat(z0))), MARK(U22(isNat(z0)))) A__U61(tt, U22(U31(z0, z1))) -> c26(A__LENGTH(a__U22(a__U31(mark(z0), z1))), MARK(U22(U31(z0, z1)))) A__U61(tt, U22(U32(z0))) -> c26(A__LENGTH(a__U22(a__U32(mark(z0)))), MARK(U22(U32(z0)))) A__U61(tt, U22(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U22(a__U41(mark(z0), z1, z2))), MARK(U22(U41(z0, z1, z2)))) A__U61(tt, U22(U42(z0, z1))) -> c26(A__LENGTH(a__U22(a__U42(mark(z0), z1))), MARK(U22(U42(z0, z1)))) A__U61(tt, U22(U43(z0))) -> c26(A__LENGTH(a__U22(a__U43(mark(z0)))), MARK(U22(U43(z0)))) A__U61(tt, U22(isNatIList(z0))) -> c26(A__LENGTH(a__U22(a__isNatIList(z0))), MARK(U22(isNatIList(z0)))) A__U61(tt, U22(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U22(a__U51(mark(z0), z1, z2))), MARK(U22(U51(z0, z1, z2)))) A__U61(tt, U22(U52(z0, z1))) -> c26(A__LENGTH(a__U22(a__U52(mark(z0), z1))), MARK(U22(U52(z0, z1)))) A__U61(tt, U22(U53(z0))) -> c26(A__LENGTH(a__U22(a__U53(mark(z0)))), MARK(U22(U53(z0)))) A__U61(tt, U22(U61(z0, z1))) -> c26(A__LENGTH(a__U22(a__U61(mark(z0), z1))), MARK(U22(U61(z0, z1)))) A__U61(tt, U22(length(z0))) -> c26(A__LENGTH(a__U22(a__length(mark(z0)))), MARK(U22(length(z0)))) 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A__U61(tt, U42(x0, z1)) -> c26(MARK(U42(x0, z1))) A__U61(tt, U42(0, x1)) -> c26(A__LENGTH(a__U42(0, x1))) A__U61(tt, U42(nil, x1)) -> c26(A__LENGTH(a__U42(nil, x1))) A__U61(tt, U43(zeros)) -> c26(A__LENGTH(a__U43(a__zeros)), MARK(U43(zeros))) A__U61(tt, U43(U11(z0, z1))) -> c26(A__LENGTH(a__U43(a__U11(mark(z0), z1))), MARK(U43(U11(z0, z1)))) A__U61(tt, U43(U12(z0))) -> c26(A__LENGTH(a__U43(a__U12(mark(z0)))), MARK(U43(U12(z0)))) A__U61(tt, U43(isNatList(z0))) -> c26(A__LENGTH(a__U43(a__isNatList(z0))), MARK(U43(isNatList(z0)))) A__U61(tt, U43(U21(z0, z1))) -> c26(A__LENGTH(a__U43(a__U21(mark(z0), z1))), MARK(U43(U21(z0, z1)))) A__U61(tt, U43(U22(z0))) -> c26(A__LENGTH(a__U43(a__U22(mark(z0)))), MARK(U43(U22(z0)))) A__U61(tt, U43(isNat(z0))) -> c26(A__LENGTH(a__U43(a__isNat(z0))), MARK(U43(isNat(z0)))) A__U61(tt, U43(U31(z0, z1))) -> c26(A__LENGTH(a__U43(a__U31(mark(z0), z1))), MARK(U43(U31(z0, z1)))) A__U61(tt, U43(U32(z0))) -> c26(A__LENGTH(a__U43(a__U32(mark(z0)))), 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z1))), MARK(U43(and(z0, z1)))) A__U61(tt, U43(isNatIListKind(z0))) -> c26(A__LENGTH(a__U43(a__isNatIListKind(z0))), MARK(U43(isNatIListKind(z0)))) A__U61(tt, U43(isNatKind(z0))) -> c26(A__LENGTH(a__U43(a__isNatKind(z0))), MARK(U43(isNatKind(z0)))) A__U61(tt, U43(cons(z0, z1))) -> c26(A__LENGTH(a__U43(cons(mark(z0), z1))), MARK(U43(cons(z0, z1)))) A__U61(tt, U43(0)) -> c26(A__LENGTH(a__U43(0)), MARK(U43(0))) A__U61(tt, U43(tt)) -> c26(A__LENGTH(a__U43(tt)), MARK(U43(tt))) A__U61(tt, U43(s(z0))) -> c26(A__LENGTH(a__U43(s(mark(z0)))), MARK(U43(s(z0)))) A__U61(tt, U43(nil)) -> c26(A__LENGTH(a__U43(nil)), MARK(U43(nil))) A__U61(tt, U43(x0)) -> c26(MARK(U43(x0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__U31(a__isNatIListKind(z0), z0)), MARK(isNatIList(z0))) A__U61(tt, isNatIList(cons(z0, z1))) -> c26(A__LENGTH(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatIList(cons(z0, z1)))) A__U61(tt, isNatIList(zeros)) -> c26(MARK(isNatIList(zeros))) A__U61(tt, isNatIList(z0)) -> c26(MARK(isNatIList(z0))) A__U61(tt, U51(zeros, x1, x2)) -> c26(A__LENGTH(a__U51(a__zeros, x1, x2)), MARK(U51(zeros, x1, x2))) A__U61(tt, U51(U11(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U11(mark(z0), z1), x1, x2)), MARK(U51(U11(z0, z1), x1, x2))) A__U61(tt, U51(U12(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U12(mark(z0)), x1, x2)), MARK(U51(U12(z0), x1, x2))) A__U61(tt, U51(isNatList(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatList(z0), x1, x2)), MARK(U51(isNatList(z0), x1, x2))) A__U61(tt, U51(U21(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U21(mark(z0), z1), x1, x2)), MARK(U51(U21(z0, z1), x1, x2))) A__U61(tt, U51(U22(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U22(mark(z0)), x1, x2)), MARK(U51(U22(z0), x1, x2))) A__U61(tt, U51(isNat(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNat(z0), x1, x2)), MARK(U51(isNat(z0), x1, x2))) A__U61(tt, U51(U31(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U31(mark(z0), z1), x1, x2)), MARK(U51(U31(z0, z1), x1, x2))) A__U61(tt, U51(U32(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U32(mark(z0)), x1, x2)), MARK(U51(U32(z0), x1, x2))) A__U61(tt, U51(U41(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U51(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U51(U41(z0, z1, z2), x1, x2))) A__U61(tt, U51(U42(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U42(mark(z0), z1), x1, x2)), MARK(U51(U42(z0, z1), x1, x2))) A__U61(tt, U51(U43(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U43(mark(z0)), x1, x2)), MARK(U51(U43(z0), x1, x2))) A__U61(tt, U51(isNatIList(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatIList(z0), x1, x2)), MARK(U51(isNatIList(z0), x1, x2))) A__U61(tt, U51(U51(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U51(a__U51(mark(z0), z1, z2), x1, x2)), MARK(U51(U51(z0, z1, z2), x1, x2))) A__U61(tt, U51(U52(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U52(mark(z0), z1), x1, x2)), MARK(U51(U52(z0, z1), x1, x2))) A__U61(tt, U51(U53(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U53(mark(z0)), x1, x2)), MARK(U51(U53(z0), x1, x2))) A__U61(tt, U51(U61(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U61(mark(z0), z1), x1, x2)), MARK(U51(U61(z0, z1), x1, x2))) A__U61(tt, U51(length(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__length(mark(z0)), x1, x2)), MARK(U51(length(z0), x1, x2))) A__U61(tt, U51(and(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__and(mark(z0), z1), x1, x2)), MARK(U51(and(z0, z1), x1, x2))) A__U61(tt, U51(isNatIListKind(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatIListKind(z0), x1, x2)), MARK(U51(isNatIListKind(z0), x1, x2))) A__U61(tt, U51(isNatKind(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatKind(z0), x1, x2)), MARK(U51(isNatKind(z0), x1, x2))) A__U61(tt, U51(cons(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(cons(mark(z0), z1), x1, x2)), MARK(U51(cons(z0, z1), x1, x2))) A__U61(tt, U51(tt, x1, x2)) -> c26(A__LENGTH(a__U51(tt, x1, x2)), MARK(U51(tt, x1, x2))) A__U61(tt, U51(s(z0), x1, x2)) -> c26(A__LENGTH(a__U51(s(mark(z0)), x1, x2)), MARK(U51(s(z0), x1, x2))) A__U61(tt, U51(x0, z1, z2)) -> c26(MARK(U51(x0, z1, z2))) A__U61(tt, U51(0, x1, x2)) -> c26(A__LENGTH(a__U51(0, x1, x2))) A__U61(tt, U51(nil, x1, x2)) -> c26(A__LENGTH(a__U51(nil, x1, x2))) A__U61(tt, U52(zeros, x1)) -> c26(A__LENGTH(a__U52(a__zeros, x1)), MARK(U52(zeros, x1))) A__U61(tt, U52(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U11(mark(z0), z1), x1)), MARK(U52(U11(z0, z1), x1))) A__U61(tt, U52(U12(z0), x1)) -> c26(A__LENGTH(a__U52(a__U12(mark(z0)), x1)), MARK(U52(U12(z0), x1))) A__U61(tt, U52(isNatList(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatList(z0), x1)), MARK(U52(isNatList(z0), x1))) A__U61(tt, U52(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U21(mark(z0), z1), x1)), MARK(U52(U21(z0, z1), x1))) A__U61(tt, U52(U22(z0), x1)) -> c26(A__LENGTH(a__U52(a__U22(mark(z0)), x1)), MARK(U52(U22(z0), x1))) A__U61(tt, U52(isNat(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNat(z0), x1)), MARK(U52(isNat(z0), x1))) A__U61(tt, U52(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U31(mark(z0), z1), x1)), MARK(U52(U31(z0, z1), x1))) A__U61(tt, U52(U32(z0), x1)) -> c26(A__LENGTH(a__U52(a__U32(mark(z0)), x1)), MARK(U52(U32(z0), x1))) A__U61(tt, U52(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U52(a__U41(mark(z0), z1, z2), x1)), MARK(U52(U41(z0, z1, z2), x1))) A__U61(tt, U52(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U42(mark(z0), z1), x1)), MARK(U52(U42(z0, z1), x1))) A__U61(tt, U52(U43(z0), x1)) -> c26(A__LENGTH(a__U52(a__U43(mark(z0)), x1)), MARK(U52(U43(z0), x1))) A__U61(tt, U52(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatIList(z0), x1)), MARK(U52(isNatIList(z0), x1))) A__U61(tt, U52(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U52(a__U51(mark(z0), z1, z2), x1)), MARK(U52(U51(z0, z1, z2), x1))) A__U61(tt, U52(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U52(mark(z0), z1), x1)), MARK(U52(U52(z0, z1), x1))) A__U61(tt, U52(U53(z0), x1)) -> c26(A__LENGTH(a__U52(a__U53(mark(z0)), x1)), MARK(U52(U53(z0), x1))) A__U61(tt, U52(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U61(mark(z0), z1), x1)), MARK(U52(U61(z0, z1), x1))) A__U61(tt, U52(length(z0), x1)) -> c26(A__LENGTH(a__U52(a__length(mark(z0)), x1)), MARK(U52(length(z0), x1))) A__U61(tt, U52(and(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__and(mark(z0), z1), x1)), MARK(U52(and(z0, z1), x1))) A__U61(tt, U52(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatIListKind(z0), x1)), MARK(U52(isNatIListKind(z0), x1))) A__U61(tt, U52(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatKind(z0), x1)), MARK(U52(isNatKind(z0), x1))) A__U61(tt, U52(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U52(cons(mark(z0), z1), x1)), MARK(U52(cons(z0, z1), x1))) A__U61(tt, U52(tt, x1)) -> c26(A__LENGTH(a__U52(tt, x1)), MARK(U52(tt, x1))) A__U61(tt, U52(s(z0), x1)) -> c26(A__LENGTH(a__U52(s(mark(z0)), x1)), MARK(U52(s(z0), x1))) A__U61(tt, U52(x0, z1)) -> c26(MARK(U52(x0, z1))) A__U61(tt, U52(0, x1)) -> c26(A__LENGTH(a__U52(0, x1))) A__U61(tt, U52(nil, x1)) -> c26(A__LENGTH(a__U52(nil, x1))) A__U61(tt, U53(zeros)) -> c26(A__LENGTH(a__U53(a__zeros)), MARK(U53(zeros))) A__U61(tt, U53(U11(z0, z1))) -> c26(A__LENGTH(a__U53(a__U11(mark(z0), z1))), MARK(U53(U11(z0, z1)))) A__U61(tt, U53(U12(z0))) -> c26(A__LENGTH(a__U53(a__U12(mark(z0)))), MARK(U53(U12(z0)))) A__U61(tt, U53(isNatList(z0))) -> c26(A__LENGTH(a__U53(a__isNatList(z0))), MARK(U53(isNatList(z0)))) A__U61(tt, U53(U21(z0, z1))) -> c26(A__LENGTH(a__U53(a__U21(mark(z0), z1))), MARK(U53(U21(z0, z1)))) A__U61(tt, U53(U22(z0))) -> c26(A__LENGTH(a__U53(a__U22(mark(z0)))), MARK(U53(U22(z0)))) A__U61(tt, U53(isNat(z0))) -> c26(A__LENGTH(a__U53(a__isNat(z0))), MARK(U53(isNat(z0)))) A__U61(tt, U53(U31(z0, z1))) -> c26(A__LENGTH(a__U53(a__U31(mark(z0), z1))), MARK(U53(U31(z0, z1)))) A__U61(tt, U53(U32(z0))) -> c26(A__LENGTH(a__U53(a__U32(mark(z0)))), MARK(U53(U32(z0)))) A__U61(tt, U53(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U53(a__U41(mark(z0), z1, z2))), MARK(U53(U41(z0, z1, z2)))) A__U61(tt, U53(U42(z0, z1))) -> c26(A__LENGTH(a__U53(a__U42(mark(z0), z1))), MARK(U53(U42(z0, z1)))) A__U61(tt, U53(U43(z0))) -> c26(A__LENGTH(a__U53(a__U43(mark(z0)))), MARK(U53(U43(z0)))) A__U61(tt, U53(isNatIList(z0))) -> c26(A__LENGTH(a__U53(a__isNatIList(z0))), MARK(U53(isNatIList(z0)))) A__U61(tt, U53(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U53(a__U51(mark(z0), z1, z2))), MARK(U53(U51(z0, z1, z2)))) A__U61(tt, U53(U52(z0, z1))) -> c26(A__LENGTH(a__U53(a__U52(mark(z0), z1))), MARK(U53(U52(z0, z1)))) A__U61(tt, U53(U53(z0))) -> c26(A__LENGTH(a__U53(a__U53(mark(z0)))), MARK(U53(U53(z0)))) A__U61(tt, U53(U61(z0, z1))) -> c26(A__LENGTH(a__U53(a__U61(mark(z0), z1))), MARK(U53(U61(z0, z1)))) A__U61(tt, U53(length(z0))) -> c26(A__LENGTH(a__U53(a__length(mark(z0)))), MARK(U53(length(z0)))) A__U61(tt, U53(and(z0, z1))) -> c26(A__LENGTH(a__U53(a__and(mark(z0), z1))), MARK(U53(and(z0, z1)))) A__U61(tt, U53(isNatIListKind(z0))) -> c26(A__LENGTH(a__U53(a__isNatIListKind(z0))), MARK(U53(isNatIListKind(z0)))) A__U61(tt, U53(isNatKind(z0))) -> c26(A__LENGTH(a__U53(a__isNatKind(z0))), MARK(U53(isNatKind(z0)))) A__U61(tt, U53(cons(z0, z1))) -> c26(A__LENGTH(a__U53(cons(mark(z0), z1))), MARK(U53(cons(z0, z1)))) A__U61(tt, U53(0)) -> c26(A__LENGTH(a__U53(0)), MARK(U53(0))) A__U61(tt, U53(tt)) -> c26(A__LENGTH(a__U53(tt)), MARK(U53(tt))) A__U61(tt, U53(s(z0))) -> c26(A__LENGTH(a__U53(s(mark(z0)))), MARK(U53(s(z0)))) A__U61(tt, U53(nil)) -> c26(A__LENGTH(a__U53(nil)), MARK(U53(nil))) A__U61(tt, U53(x0)) -> c26(MARK(U53(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_1, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c14_2, c20_2 ---------------------------------------- (207) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U61(tt, U61(z0, z1)) -> c26(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) by A__U61(tt, U61(x0, z1)) -> c26(A__LENGTH(U61(mark(x0), z1)), MARK(U61(x0, z1))) A__U61(tt, U61(zeros, x1)) -> c26(A__LENGTH(a__U61(a__zeros, x1)), MARK(U61(zeros, x1))) A__U61(tt, U61(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U61(a__U11(mark(z0), z1), x1)), MARK(U61(U11(z0, z1), x1))) A__U61(tt, U61(U12(z0), x1)) -> c26(A__LENGTH(a__U61(a__U12(mark(z0)), x1)), MARK(U61(U12(z0), x1))) A__U61(tt, U61(isNatList(z0), x1)) -> c26(A__LENGTH(a__U61(a__isNatList(z0), x1)), MARK(U61(isNatList(z0), x1))) A__U61(tt, U61(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U61(a__U21(mark(z0), z1), x1)), MARK(U61(U21(z0, z1), x1))) A__U61(tt, U61(U22(z0), x1)) -> c26(A__LENGTH(a__U61(a__U22(mark(z0)), x1)), MARK(U61(U22(z0), x1))) A__U61(tt, U61(isNat(z0), x1)) -> c26(A__LENGTH(a__U61(a__isNat(z0), x1)), MARK(U61(isNat(z0), x1))) A__U61(tt, U61(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U61(a__U31(mark(z0), z1), x1)), MARK(U61(U31(z0, z1), x1))) A__U61(tt, U61(U32(z0), x1)) -> c26(A__LENGTH(a__U61(a__U32(mark(z0)), x1)), MARK(U61(U32(z0), x1))) A__U61(tt, U61(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U61(a__U41(mark(z0), z1, z2), x1)), MARK(U61(U41(z0, z1, z2), x1))) A__U61(tt, U61(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U61(a__U42(mark(z0), z1), x1)), MARK(U61(U42(z0, z1), x1))) A__U61(tt, U61(U43(z0), x1)) -> c26(A__LENGTH(a__U61(a__U43(mark(z0)), x1)), MARK(U61(U43(z0), x1))) A__U61(tt, U61(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U61(a__isNatIList(z0), x1)), MARK(U61(isNatIList(z0), x1))) A__U61(tt, U61(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U61(a__U51(mark(z0), z1, z2), x1)), MARK(U61(U51(z0, z1, z2), x1))) A__U61(tt, U61(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U61(a__U52(mark(z0), z1), x1)), MARK(U61(U52(z0, z1), x1))) A__U61(tt, U61(U53(z0), x1)) -> c26(A__LENGTH(a__U61(a__U53(mark(z0)), x1)), MARK(U61(U53(z0), x1))) A__U61(tt, U61(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U61(a__U61(mark(z0), z1), x1)), MARK(U61(U61(z0, z1), x1))) A__U61(tt, U61(length(z0), x1)) -> c26(A__LENGTH(a__U61(a__length(mark(z0)), x1)), MARK(U61(length(z0), x1))) A__U61(tt, U61(and(z0, z1), x1)) -> c26(A__LENGTH(a__U61(a__and(mark(z0), z1), x1)), MARK(U61(and(z0, z1), x1))) A__U61(tt, U61(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U61(a__isNatIListKind(z0), x1)), MARK(U61(isNatIListKind(z0), x1))) A__U61(tt, U61(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U61(a__isNatKind(z0), x1)), MARK(U61(isNatKind(z0), x1))) A__U61(tt, U61(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U61(cons(mark(z0), z1), x1)), MARK(U61(cons(z0, z1), x1))) A__U61(tt, U61(0, x1)) -> c26(A__LENGTH(a__U61(0, x1)), MARK(U61(0, x1))) A__U61(tt, U61(tt, x1)) -> c26(A__LENGTH(a__U61(tt, x1)), MARK(U61(tt, x1))) A__U61(tt, U61(s(z0), x1)) -> c26(A__LENGTH(a__U61(s(mark(z0)), x1)), MARK(U61(s(z0), x1))) A__U61(tt, U61(nil, x1)) -> c26(A__LENGTH(a__U61(nil, x1)), MARK(U61(nil, x1))) ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) 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x1))) A__U61(tt, U52(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U52(mark(z0), z1), x1)), MARK(U52(U52(z0, z1), x1))) A__U61(tt, U52(U53(z0), x1)) -> c26(A__LENGTH(a__U52(a__U53(mark(z0)), x1)), MARK(U52(U53(z0), x1))) A__U61(tt, U52(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U61(mark(z0), z1), x1)), MARK(U52(U61(z0, z1), x1))) A__U61(tt, U52(length(z0), x1)) -> c26(A__LENGTH(a__U52(a__length(mark(z0)), x1)), MARK(U52(length(z0), x1))) A__U61(tt, U52(and(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__and(mark(z0), z1), x1)), MARK(U52(and(z0, z1), x1))) A__U61(tt, U52(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatIListKind(z0), x1)), MARK(U52(isNatIListKind(z0), x1))) A__U61(tt, U52(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatKind(z0), x1)), MARK(U52(isNatKind(z0), x1))) A__U61(tt, U52(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U52(cons(mark(z0), z1), x1)), MARK(U52(cons(z0, z1), x1))) A__U61(tt, U52(tt, x1)) -> c26(A__LENGTH(a__U52(tt, x1)), MARK(U52(tt, x1))) A__U61(tt, U52(s(z0), x1)) -> c26(A__LENGTH(a__U52(s(mark(z0)), x1)), MARK(U52(s(z0), x1))) A__U61(tt, U52(x0, z1)) -> c26(MARK(U52(x0, z1))) A__U61(tt, U52(0, x1)) -> c26(A__LENGTH(a__U52(0, x1))) A__U61(tt, U52(nil, x1)) -> c26(A__LENGTH(a__U52(nil, x1))) A__U61(tt, U53(zeros)) -> c26(A__LENGTH(a__U53(a__zeros)), MARK(U53(zeros))) A__U61(tt, U53(U11(z0, z1))) -> c26(A__LENGTH(a__U53(a__U11(mark(z0), z1))), MARK(U53(U11(z0, z1)))) A__U61(tt, U53(U12(z0))) -> c26(A__LENGTH(a__U53(a__U12(mark(z0)))), MARK(U53(U12(z0)))) A__U61(tt, U53(isNatList(z0))) -> c26(A__LENGTH(a__U53(a__isNatList(z0))), MARK(U53(isNatList(z0)))) A__U61(tt, U53(U21(z0, z1))) -> c26(A__LENGTH(a__U53(a__U21(mark(z0), z1))), MARK(U53(U21(z0, z1)))) A__U61(tt, U53(U22(z0))) -> c26(A__LENGTH(a__U53(a__U22(mark(z0)))), MARK(U53(U22(z0)))) A__U61(tt, U53(isNat(z0))) -> c26(A__LENGTH(a__U53(a__isNat(z0))), MARK(U53(isNat(z0)))) A__U61(tt, U53(U31(z0, z1))) -> c26(A__LENGTH(a__U53(a__U31(mark(z0), z1))), MARK(U53(U31(z0, z1)))) A__U61(tt, U53(U32(z0))) -> c26(A__LENGTH(a__U53(a__U32(mark(z0)))), MARK(U53(U32(z0)))) A__U61(tt, U53(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U53(a__U41(mark(z0), z1, z2))), MARK(U53(U41(z0, z1, z2)))) A__U61(tt, U53(U42(z0, z1))) -> c26(A__LENGTH(a__U53(a__U42(mark(z0), z1))), MARK(U53(U42(z0, z1)))) A__U61(tt, U53(U43(z0))) -> c26(A__LENGTH(a__U53(a__U43(mark(z0)))), MARK(U53(U43(z0)))) A__U61(tt, U53(isNatIList(z0))) -> c26(A__LENGTH(a__U53(a__isNatIList(z0))), MARK(U53(isNatIList(z0)))) A__U61(tt, U53(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U53(a__U51(mark(z0), z1, z2))), MARK(U53(U51(z0, z1, z2)))) A__U61(tt, U53(U52(z0, z1))) -> c26(A__LENGTH(a__U53(a__U52(mark(z0), z1))), MARK(U53(U52(z0, z1)))) A__U61(tt, U53(U53(z0))) -> c26(A__LENGTH(a__U53(a__U53(mark(z0)))), MARK(U53(U53(z0)))) A__U61(tt, U53(U61(z0, z1))) -> c26(A__LENGTH(a__U53(a__U61(mark(z0), z1))), MARK(U53(U61(z0, z1)))) A__U61(tt, U53(length(z0))) -> c26(A__LENGTH(a__U53(a__length(mark(z0)))), MARK(U53(length(z0)))) A__U61(tt, U53(and(z0, z1))) -> c26(A__LENGTH(a__U53(a__and(mark(z0), z1))), MARK(U53(and(z0, z1)))) A__U61(tt, U53(isNatIListKind(z0))) -> c26(A__LENGTH(a__U53(a__isNatIListKind(z0))), MARK(U53(isNatIListKind(z0)))) A__U61(tt, U53(isNatKind(z0))) -> c26(A__LENGTH(a__U53(a__isNatKind(z0))), MARK(U53(isNatKind(z0)))) A__U61(tt, U53(cons(z0, z1))) -> c26(A__LENGTH(a__U53(cons(mark(z0), z1))), MARK(U53(cons(z0, z1)))) A__U61(tt, U53(0)) -> c26(A__LENGTH(a__U53(0)), MARK(U53(0))) A__U61(tt, U53(tt)) -> c26(A__LENGTH(a__U53(tt)), MARK(U53(tt))) A__U61(tt, U53(s(z0))) -> c26(A__LENGTH(a__U53(s(mark(z0)))), MARK(U53(s(z0)))) A__U61(tt, U53(nil)) -> c26(A__LENGTH(a__U53(nil)), MARK(U53(nil))) A__U61(tt, U53(x0)) -> c26(MARK(U53(x0))) A__U61(tt, U61(x0, z1)) -> c26(A__LENGTH(U61(mark(x0), z1)), MARK(U61(x0, z1))) A__U61(tt, U61(zeros, x1)) -> c26(A__LENGTH(a__U61(a__zeros, x1)), MARK(U61(zeros, x1))) A__U61(tt, U61(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U61(a__U11(mark(z0), z1), x1)), MARK(U61(U11(z0, z1), x1))) A__U61(tt, U61(U12(z0), x1)) -> c26(A__LENGTH(a__U61(a__U12(mark(z0)), x1)), MARK(U61(U12(z0), x1))) A__U61(tt, U61(isNatList(z0), x1)) -> c26(A__LENGTH(a__U61(a__isNatList(z0), x1)), MARK(U61(isNatList(z0), x1))) A__U61(tt, U61(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U61(a__U21(mark(z0), z1), x1)), MARK(U61(U21(z0, z1), x1))) A__U61(tt, U61(U22(z0), x1)) -> c26(A__LENGTH(a__U61(a__U22(mark(z0)), x1)), MARK(U61(U22(z0), x1))) A__U61(tt, U61(isNat(z0), x1)) -> c26(A__LENGTH(a__U61(a__isNat(z0), x1)), MARK(U61(isNat(z0), x1))) A__U61(tt, U61(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U61(a__U31(mark(z0), z1), x1)), MARK(U61(U31(z0, z1), x1))) A__U61(tt, U61(U32(z0), x1)) -> c26(A__LENGTH(a__U61(a__U32(mark(z0)), x1)), MARK(U61(U32(z0), x1))) A__U61(tt, U61(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U61(a__U41(mark(z0), z1, z2), x1)), MARK(U61(U41(z0, z1, z2), x1))) A__U61(tt, U61(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U61(a__U42(mark(z0), z1), x1)), MARK(U61(U42(z0, z1), x1))) A__U61(tt, U61(U43(z0), x1)) -> c26(A__LENGTH(a__U61(a__U43(mark(z0)), x1)), MARK(U61(U43(z0), x1))) A__U61(tt, U61(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U61(a__isNatIList(z0), x1)), MARK(U61(isNatIList(z0), x1))) A__U61(tt, U61(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U61(a__U51(mark(z0), z1, z2), x1)), MARK(U61(U51(z0, z1, z2), x1))) A__U61(tt, U61(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U61(a__U52(mark(z0), z1), x1)), MARK(U61(U52(z0, z1), x1))) A__U61(tt, U61(U53(z0), x1)) -> c26(A__LENGTH(a__U61(a__U53(mark(z0)), x1)), MARK(U61(U53(z0), x1))) A__U61(tt, U61(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U61(a__U61(mark(z0), z1), x1)), MARK(U61(U61(z0, z1), x1))) A__U61(tt, U61(length(z0), x1)) -> c26(A__LENGTH(a__U61(a__length(mark(z0)), x1)), MARK(U61(length(z0), x1))) A__U61(tt, U61(and(z0, z1), x1)) -> c26(A__LENGTH(a__U61(a__and(mark(z0), z1), x1)), MARK(U61(and(z0, z1), x1))) A__U61(tt, U61(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U61(a__isNatIListKind(z0), x1)), MARK(U61(isNatIListKind(z0), x1))) A__U61(tt, U61(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U61(a__isNatKind(z0), x1)), MARK(U61(isNatKind(z0), x1))) A__U61(tt, U61(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U61(cons(mark(z0), z1), x1)), MARK(U61(cons(z0, z1), x1))) A__U61(tt, U61(0, x1)) -> c26(A__LENGTH(a__U61(0, x1)), MARK(U61(0, x1))) A__U61(tt, U61(tt, x1)) -> c26(A__LENGTH(a__U61(tt, x1)), MARK(U61(tt, x1))) A__U61(tt, U61(s(z0), x1)) -> c26(A__LENGTH(a__U61(s(mark(z0)), x1)), MARK(U61(s(z0), x1))) A__U61(tt, U61(nil, x1)) -> c26(A__LENGTH(a__U61(nil, x1)), MARK(U61(nil, x1))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> 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x2))) A__U61(tt, U51(isNatIList(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatIList(z0), x1, x2)), MARK(U51(isNatIList(z0), x1, x2))) A__U61(tt, U51(U51(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U51(a__U51(mark(z0), z1, z2), x1, x2)), MARK(U51(U51(z0, z1, z2), x1, x2))) A__U61(tt, U51(U52(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U52(mark(z0), z1), x1, x2)), MARK(U51(U52(z0, z1), x1, x2))) A__U61(tt, U51(U53(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U53(mark(z0)), x1, x2)), MARK(U51(U53(z0), x1, x2))) A__U61(tt, U51(U61(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U61(mark(z0), z1), x1, x2)), MARK(U51(U61(z0, z1), x1, x2))) A__U61(tt, U51(length(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__length(mark(z0)), x1, x2)), MARK(U51(length(z0), x1, x2))) A__U61(tt, U51(and(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__and(mark(z0), z1), x1, x2)), MARK(U51(and(z0, z1), x1, x2))) A__U61(tt, U51(isNatIListKind(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatIListKind(z0), x1, x2)), MARK(U51(isNatIListKind(z0), x1, x2))) A__U61(tt, U51(isNatKind(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatKind(z0), x1, x2)), MARK(U51(isNatKind(z0), x1, x2))) A__U61(tt, U51(cons(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(cons(mark(z0), z1), x1, x2)), MARK(U51(cons(z0, z1), x1, x2))) A__U61(tt, U51(tt, x1, x2)) -> c26(A__LENGTH(a__U51(tt, x1, x2)), MARK(U51(tt, x1, x2))) A__U61(tt, U51(s(z0), x1, x2)) -> c26(A__LENGTH(a__U51(s(mark(z0)), x1, x2)), MARK(U51(s(z0), x1, x2))) A__U61(tt, U51(x0, z1, z2)) -> c26(MARK(U51(x0, z1, z2))) A__U61(tt, U51(0, x1, x2)) -> c26(A__LENGTH(a__U51(0, x1, x2))) A__U61(tt, U51(nil, x1, x2)) -> c26(A__LENGTH(a__U51(nil, x1, x2))) A__U61(tt, U52(zeros, x1)) -> c26(A__LENGTH(a__U52(a__zeros, x1)), MARK(U52(zeros, x1))) A__U61(tt, U52(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U11(mark(z0), z1), x1)), MARK(U52(U11(z0, z1), x1))) A__U61(tt, U52(U12(z0), x1)) -> c26(A__LENGTH(a__U52(a__U12(mark(z0)), x1)), MARK(U52(U12(z0), x1))) A__U61(tt, U52(isNatList(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatList(z0), x1)), MARK(U52(isNatList(z0), x1))) A__U61(tt, U52(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U21(mark(z0), z1), x1)), MARK(U52(U21(z0, z1), x1))) A__U61(tt, U52(U22(z0), x1)) -> c26(A__LENGTH(a__U52(a__U22(mark(z0)), x1)), MARK(U52(U22(z0), x1))) A__U61(tt, U52(isNat(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNat(z0), x1)), MARK(U52(isNat(z0), x1))) A__U61(tt, U52(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U31(mark(z0), z1), x1)), MARK(U52(U31(z0, z1), x1))) A__U61(tt, U52(U32(z0), x1)) -> c26(A__LENGTH(a__U52(a__U32(mark(z0)), x1)), MARK(U52(U32(z0), x1))) A__U61(tt, U52(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U52(a__U41(mark(z0), z1, z2), x1)), MARK(U52(U41(z0, z1, z2), x1))) A__U61(tt, U52(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U42(mark(z0), z1), x1)), MARK(U52(U42(z0, z1), x1))) A__U61(tt, U52(U43(z0), x1)) -> c26(A__LENGTH(a__U52(a__U43(mark(z0)), x1)), MARK(U52(U43(z0), x1))) A__U61(tt, U52(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatIList(z0), x1)), MARK(U52(isNatIList(z0), x1))) A__U61(tt, U52(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U52(a__U51(mark(z0), z1, z2), x1)), MARK(U52(U51(z0, z1, z2), x1))) A__U61(tt, U52(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U52(mark(z0), z1), x1)), MARK(U52(U52(z0, z1), x1))) A__U61(tt, U52(U53(z0), x1)) -> c26(A__LENGTH(a__U52(a__U53(mark(z0)), x1)), MARK(U52(U53(z0), x1))) A__U61(tt, U52(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U61(mark(z0), z1), x1)), MARK(U52(U61(z0, z1), x1))) A__U61(tt, U52(length(z0), x1)) -> c26(A__LENGTH(a__U52(a__length(mark(z0)), x1)), MARK(U52(length(z0), x1))) A__U61(tt, U52(and(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__and(mark(z0), z1), x1)), MARK(U52(and(z0, z1), x1))) A__U61(tt, U52(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatIListKind(z0), x1)), MARK(U52(isNatIListKind(z0), x1))) A__U61(tt, U52(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatKind(z0), x1)), MARK(U52(isNatKind(z0), x1))) A__U61(tt, U52(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U52(cons(mark(z0), z1), x1)), MARK(U52(cons(z0, z1), x1))) A__U61(tt, U52(tt, x1)) -> c26(A__LENGTH(a__U52(tt, x1)), MARK(U52(tt, x1))) A__U61(tt, U52(s(z0), x1)) -> c26(A__LENGTH(a__U52(s(mark(z0)), x1)), MARK(U52(s(z0), x1))) A__U61(tt, U52(x0, z1)) -> c26(MARK(U52(x0, z1))) A__U61(tt, U52(0, x1)) -> c26(A__LENGTH(a__U52(0, x1))) A__U61(tt, U52(nil, x1)) -> c26(A__LENGTH(a__U52(nil, x1))) A__U61(tt, U53(zeros)) -> c26(A__LENGTH(a__U53(a__zeros)), MARK(U53(zeros))) A__U61(tt, U53(U11(z0, z1))) -> c26(A__LENGTH(a__U53(a__U11(mark(z0), z1))), MARK(U53(U11(z0, z1)))) A__U61(tt, U53(U12(z0))) -> c26(A__LENGTH(a__U53(a__U12(mark(z0)))), MARK(U53(U12(z0)))) A__U61(tt, U53(isNatList(z0))) -> c26(A__LENGTH(a__U53(a__isNatList(z0))), MARK(U53(isNatList(z0)))) A__U61(tt, U53(U21(z0, z1))) -> c26(A__LENGTH(a__U53(a__U21(mark(z0), z1))), MARK(U53(U21(z0, z1)))) A__U61(tt, U53(U22(z0))) -> c26(A__LENGTH(a__U53(a__U22(mark(z0)))), MARK(U53(U22(z0)))) A__U61(tt, U53(isNat(z0))) -> c26(A__LENGTH(a__U53(a__isNat(z0))), MARK(U53(isNat(z0)))) A__U61(tt, U53(U31(z0, z1))) -> c26(A__LENGTH(a__U53(a__U31(mark(z0), z1))), MARK(U53(U31(z0, z1)))) A__U61(tt, U53(U32(z0))) -> c26(A__LENGTH(a__U53(a__U32(mark(z0)))), MARK(U53(U32(z0)))) A__U61(tt, U53(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U53(a__U41(mark(z0), z1, z2))), MARK(U53(U41(z0, z1, z2)))) A__U61(tt, U53(U42(z0, z1))) -> c26(A__LENGTH(a__U53(a__U42(mark(z0), z1))), MARK(U53(U42(z0, z1)))) A__U61(tt, U53(U43(z0))) -> c26(A__LENGTH(a__U53(a__U43(mark(z0)))), MARK(U53(U43(z0)))) A__U61(tt, U53(isNatIList(z0))) -> c26(A__LENGTH(a__U53(a__isNatIList(z0))), MARK(U53(isNatIList(z0)))) A__U61(tt, U53(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U53(a__U51(mark(z0), z1, z2))), MARK(U53(U51(z0, z1, z2)))) A__U61(tt, U53(U52(z0, z1))) -> c26(A__LENGTH(a__U53(a__U52(mark(z0), z1))), MARK(U53(U52(z0, z1)))) A__U61(tt, U53(U53(z0))) -> c26(A__LENGTH(a__U53(a__U53(mark(z0)))), MARK(U53(U53(z0)))) A__U61(tt, U53(U61(z0, z1))) -> c26(A__LENGTH(a__U53(a__U61(mark(z0), z1))), MARK(U53(U61(z0, z1)))) A__U61(tt, U53(length(z0))) -> c26(A__LENGTH(a__U53(a__length(mark(z0)))), MARK(U53(length(z0)))) A__U61(tt, U53(and(z0, z1))) -> c26(A__LENGTH(a__U53(a__and(mark(z0), z1))), MARK(U53(and(z0, z1)))) A__U61(tt, U53(isNatIListKind(z0))) -> c26(A__LENGTH(a__U53(a__isNatIListKind(z0))), MARK(U53(isNatIListKind(z0)))) A__U61(tt, U53(isNatKind(z0))) -> c26(A__LENGTH(a__U53(a__isNatKind(z0))), MARK(U53(isNatKind(z0)))) A__U61(tt, U53(cons(z0, z1))) -> c26(A__LENGTH(a__U53(cons(mark(z0), z1))), MARK(U53(cons(z0, z1)))) A__U61(tt, U53(0)) -> c26(A__LENGTH(a__U53(0)), MARK(U53(0))) A__U61(tt, U53(tt)) -> c26(A__LENGTH(a__U53(tt)), MARK(U53(tt))) A__U61(tt, U53(s(z0))) -> c26(A__LENGTH(a__U53(s(mark(z0)))), MARK(U53(s(z0)))) A__U61(tt, U53(nil)) -> c26(A__LENGTH(a__U53(nil)), MARK(U53(nil))) A__U61(tt, U53(x0)) -> c26(MARK(U53(x0))) A__U61(tt, U61(x0, z1)) -> c26(A__LENGTH(U61(mark(x0), z1)), MARK(U61(x0, z1))) A__U61(tt, U61(zeros, x1)) -> c26(A__LENGTH(a__U61(a__zeros, x1)), MARK(U61(zeros, x1))) A__U61(tt, U61(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U61(a__U11(mark(z0), z1), x1)), MARK(U61(U11(z0, z1), x1))) A__U61(tt, U61(U12(z0), x1)) -> c26(A__LENGTH(a__U61(a__U12(mark(z0)), x1)), MARK(U61(U12(z0), x1))) A__U61(tt, U61(isNatList(z0), x1)) -> c26(A__LENGTH(a__U61(a__isNatList(z0), x1)), MARK(U61(isNatList(z0), x1))) A__U61(tt, U61(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U61(a__U21(mark(z0), z1), x1)), MARK(U61(U21(z0, z1), x1))) A__U61(tt, U61(U22(z0), x1)) -> c26(A__LENGTH(a__U61(a__U22(mark(z0)), x1)), MARK(U61(U22(z0), x1))) A__U61(tt, U61(isNat(z0), x1)) -> c26(A__LENGTH(a__U61(a__isNat(z0), x1)), MARK(U61(isNat(z0), x1))) A__U61(tt, U61(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U61(a__U31(mark(z0), z1), x1)), MARK(U61(U31(z0, z1), x1))) A__U61(tt, U61(U32(z0), x1)) -> c26(A__LENGTH(a__U61(a__U32(mark(z0)), x1)), MARK(U61(U32(z0), x1))) A__U61(tt, U61(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U61(a__U41(mark(z0), z1, z2), x1)), MARK(U61(U41(z0, z1, z2), x1))) A__U61(tt, U61(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U61(a__U42(mark(z0), z1), x1)), MARK(U61(U42(z0, z1), x1))) A__U61(tt, U61(U43(z0), x1)) -> c26(A__LENGTH(a__U61(a__U43(mark(z0)), x1)), MARK(U61(U43(z0), x1))) A__U61(tt, U61(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U61(a__isNatIList(z0), x1)), MARK(U61(isNatIList(z0), x1))) A__U61(tt, U61(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U61(a__U51(mark(z0), z1, z2), x1)), MARK(U61(U51(z0, z1, z2), x1))) A__U61(tt, U61(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U61(a__U52(mark(z0), z1), x1)), MARK(U61(U52(z0, z1), x1))) A__U61(tt, U61(U53(z0), x1)) -> c26(A__LENGTH(a__U61(a__U53(mark(z0)), x1)), MARK(U61(U53(z0), x1))) A__U61(tt, U61(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U61(a__U61(mark(z0), z1), x1)), MARK(U61(U61(z0, z1), x1))) A__U61(tt, U61(length(z0), x1)) -> c26(A__LENGTH(a__U61(a__length(mark(z0)), x1)), MARK(U61(length(z0), x1))) A__U61(tt, U61(and(z0, z1), x1)) -> c26(A__LENGTH(a__U61(a__and(mark(z0), z1), x1)), MARK(U61(and(z0, z1), x1))) A__U61(tt, U61(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U61(a__isNatIListKind(z0), x1)), MARK(U61(isNatIListKind(z0), x1))) A__U61(tt, U61(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U61(a__isNatKind(z0), x1)), MARK(U61(isNatKind(z0), x1))) A__U61(tt, U61(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U61(cons(mark(z0), z1), x1)), MARK(U61(cons(z0, z1), x1))) A__U61(tt, U61(0, x1)) -> c26(A__LENGTH(a__U61(0, x1)), MARK(U61(0, x1))) A__U61(tt, U61(tt, x1)) -> c26(A__LENGTH(a__U61(tt, x1)), MARK(U61(tt, x1))) A__U61(tt, U61(s(z0), x1)) -> c26(A__LENGTH(a__U61(s(mark(z0)), x1)), MARK(U61(s(z0), x1))) A__U61(tt, U61(nil, x1)) -> c26(A__LENGTH(a__U61(nil, x1)), MARK(U61(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_1, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c14_2, c20_2 ---------------------------------------- (209) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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) -> s(a__length(mark(z0))) a__U61(z0, z1) -> U61(z0, z1) 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(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(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) 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)) -> a__U61(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) 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__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, 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-> c26(A__LENGTH(a__U53(a__U51(mark(z0), z1, z2))), MARK(U53(U51(z0, z1, z2)))) A__U61(tt, U53(U52(z0, z1))) -> c26(A__LENGTH(a__U53(a__U52(mark(z0), z1))), MARK(U53(U52(z0, z1)))) A__U61(tt, U53(U53(z0))) -> c26(A__LENGTH(a__U53(a__U53(mark(z0)))), MARK(U53(U53(z0)))) A__U61(tt, U53(U61(z0, z1))) -> c26(A__LENGTH(a__U53(a__U61(mark(z0), z1))), MARK(U53(U61(z0, z1)))) A__U61(tt, U53(length(z0))) -> c26(A__LENGTH(a__U53(a__length(mark(z0)))), MARK(U53(length(z0)))) A__U61(tt, U53(and(z0, z1))) -> c26(A__LENGTH(a__U53(a__and(mark(z0), z1))), MARK(U53(and(z0, z1)))) A__U61(tt, U53(isNatIListKind(z0))) -> c26(A__LENGTH(a__U53(a__isNatIListKind(z0))), MARK(U53(isNatIListKind(z0)))) A__U61(tt, U53(isNatKind(z0))) -> c26(A__LENGTH(a__U53(a__isNatKind(z0))), MARK(U53(isNatKind(z0)))) A__U61(tt, U53(cons(z0, z1))) -> c26(A__LENGTH(a__U53(cons(mark(z0), z1))), MARK(U53(cons(z0, z1)))) A__U61(tt, U53(0)) -> c26(A__LENGTH(a__U53(0)), MARK(U53(0))) A__U61(tt, U53(tt)) -> c26(A__LENGTH(a__U53(tt)), MARK(U53(tt))) A__U61(tt, U53(s(z0))) -> c26(A__LENGTH(a__U53(s(mark(z0)))), MARK(U53(s(z0)))) A__U61(tt, U53(nil)) -> c26(A__LENGTH(a__U53(nil)), MARK(U53(nil))) A__U61(tt, U53(x0)) -> c26(MARK(U53(x0))) A__U61(tt, U61(zeros, x1)) -> c26(A__LENGTH(a__U61(a__zeros, x1)), MARK(U61(zeros, x1))) A__U61(tt, U61(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U61(a__U11(mark(z0), z1), x1)), MARK(U61(U11(z0, z1), x1))) A__U61(tt, U61(U12(z0), x1)) -> c26(A__LENGTH(a__U61(a__U12(mark(z0)), x1)), MARK(U61(U12(z0), x1))) A__U61(tt, U61(isNatList(z0), x1)) -> c26(A__LENGTH(a__U61(a__isNatList(z0), x1)), MARK(U61(isNatList(z0), x1))) A__U61(tt, U61(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U61(a__U21(mark(z0), z1), x1)), MARK(U61(U21(z0, z1), x1))) A__U61(tt, U61(U22(z0), x1)) -> c26(A__LENGTH(a__U61(a__U22(mark(z0)), x1)), MARK(U61(U22(z0), x1))) A__U61(tt, U61(isNat(z0), x1)) -> c26(A__LENGTH(a__U61(a__isNat(z0), x1)), MARK(U61(isNat(z0), x1))) A__U61(tt, U61(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U61(a__U31(mark(z0), z1), x1)), MARK(U61(U31(z0, z1), x1))) A__U61(tt, U61(U32(z0), x1)) -> c26(A__LENGTH(a__U61(a__U32(mark(z0)), x1)), MARK(U61(U32(z0), x1))) A__U61(tt, U61(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U61(a__U41(mark(z0), z1, z2), x1)), MARK(U61(U41(z0, z1, z2), x1))) A__U61(tt, U61(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U61(a__U42(mark(z0), z1), x1)), MARK(U61(U42(z0, z1), x1))) A__U61(tt, U61(U43(z0), x1)) -> c26(A__LENGTH(a__U61(a__U43(mark(z0)), x1)), MARK(U61(U43(z0), x1))) A__U61(tt, U61(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U61(a__isNatIList(z0), x1)), MARK(U61(isNatIList(z0), x1))) A__U61(tt, U61(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U61(a__U51(mark(z0), z1, z2), x1)), MARK(U61(U51(z0, z1, z2), x1))) A__U61(tt, U61(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U61(a__U52(mark(z0), z1), x1)), MARK(U61(U52(z0, z1), x1))) A__U61(tt, U61(U53(z0), x1)) -> c26(A__LENGTH(a__U61(a__U53(mark(z0)), x1)), MARK(U61(U53(z0), x1))) A__U61(tt, U61(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U61(a__U61(mark(z0), z1), x1)), MARK(U61(U61(z0, z1), x1))) A__U61(tt, U61(length(z0), x1)) -> c26(A__LENGTH(a__U61(a__length(mark(z0)), x1)), MARK(U61(length(z0), x1))) A__U61(tt, U61(and(z0, z1), x1)) -> c26(A__LENGTH(a__U61(a__and(mark(z0), z1), x1)), MARK(U61(and(z0, z1), x1))) A__U61(tt, U61(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U61(a__isNatIListKind(z0), x1)), MARK(U61(isNatIListKind(z0), x1))) A__U61(tt, U61(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U61(a__isNatKind(z0), x1)), MARK(U61(isNatKind(z0), x1))) A__U61(tt, U61(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U61(cons(mark(z0), z1), x1)), MARK(U61(cons(z0, z1), x1))) A__U61(tt, U61(tt, x1)) -> c26(A__LENGTH(a__U61(tt, x1)), MARK(U61(tt, x1))) A__U61(tt, U61(s(z0), x1)) -> c26(A__LENGTH(a__U61(s(mark(z0)), x1)), MARK(U61(s(z0), x1))) A__U61(tt, U61(x0, z1)) -> c26(MARK(U61(x0, z1))) A__U61(tt, U61(0, x1)) -> c26(A__LENGTH(a__U61(0, x1))) A__U61(tt, U61(nil, x1)) -> c26(A__LENGTH(a__U61(nil, x1))) S tuples: A__AND(tt, z0) -> c28(MARK(z0)) A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c58(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c73(MARK(z0)) MARK(s(z0)) -> c76(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)) MARK(U12(z0)) -> c54(MARK(z0)) MARK(U22(z0)) -> c57(MARK(z0)) MARK(U32(z0)) -> c60(MARK(z0)) MARK(U43(z0)) -> c63(MARK(z0)) MARK(U53(z0)) -> c67(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)) -> c26(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U61(tt, and(z0, z1)) -> c26(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U61(tt, isNatIListKind(z0)) -> c26(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U61(tt, isNatKind(z0)) -> c26(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U61(tt, cons(z0, z1)) -> c26(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U61(tt, zeros) -> c26(A__LENGTH(a__zeros)) A__U61(tt, s(z0)) -> c26(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c31(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(nil)) -> c31(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c31(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c32(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c32(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c32(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c32(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c34(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(nil) -> c34(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c34(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c36(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)) -> c36(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)) -> c36(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)) -> c36(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c36(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c40(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c40(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c40(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c47(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)) -> c47(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)) -> c47(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)) -> c47(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c47(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c50(A__U61(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))) -> c50(A__U61(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, z0)) -> c50(A__U61(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)) -> c50(A__AND(a__and(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)) -> c50(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) MARK(U11(U11(z0, z1), x1)) -> c53(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c53(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c53(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c53(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c53(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c53(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c53(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c53(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c53(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c53(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c53(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c53(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c53(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c53(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c53(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1), x1)) -> c53(A__U11(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U11(length(z0), x1)) -> c53(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(and(z0, z1), x1)) -> c53(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c53(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c53(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c53(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c53(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c53(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c53(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c56(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c56(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c56(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c56(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c56(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c56(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c56(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c56(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c56(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c56(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c56(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c56(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c56(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c56(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c56(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U21(length(z0), x1)) -> c56(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(and(z0, z1), x1)) -> c56(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c56(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c56(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c56(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c56(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c56(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c56(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c59(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c59(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c59(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c59(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c59(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c59(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c59(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c59(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c59(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c59(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c59(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c59(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c59(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c59(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c59(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1), x1)) -> c59(A__U31(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U31(length(z0), x1)) -> c59(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(and(z0, z1), x1)) -> c59(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c59(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c59(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c59(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c59(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c59(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c59(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c61(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c61(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c61(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c61(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c61(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c61(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c61(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c61(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c61(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c61(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c61(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c61(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c61(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c61(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1), x1, x2)) -> c61(A__U41(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c61(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(and(z0, z1), x1, x2)) -> c61(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c61(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c61(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c61(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c61(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c61(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c61(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c62(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c62(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c62(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c62(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c62(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c62(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c62(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c62(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c62(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c62(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c62(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c62(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c62(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c62(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c62(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1), x1)) -> c62(A__U42(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U42(length(z0), x1)) -> c62(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(and(z0, z1), x1)) -> c62(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c62(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c62(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c62(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c62(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c62(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c62(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c65(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c65(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c65(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c65(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c65(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c65(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c65(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c65(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c65(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c65(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c65(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c65(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c65(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c65(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1), x1, x2)) -> c65(A__U51(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c65(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(and(z0, z1), x1, x2)) -> c65(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c65(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c65(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c65(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c65(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c65(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c65(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c66(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c66(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c66(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c66(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c66(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c66(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c66(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c66(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c66(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c66(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c66(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c66(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c66(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c66(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c66(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1), x1)) -> c66(A__U52(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U52(length(z0), x1)) -> c66(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(and(z0, z1), x1)) -> c66(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c66(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c66(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c66(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c66(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c66(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c66(MARK(s(z0))) MARK(U61(U11(z0, z1), x1)) -> c68(A__U61(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1)) -> c68(A__U61(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U61(isNatList(z0), x1)) -> c68(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1)) -> c68(A__U61(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1)) -> c68(A__U61(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U61(isNat(z0), x1)) -> c68(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1)) -> c68(A__U61(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1)) -> c68(A__U61(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1)) -> c68(A__U61(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1)) -> c68(A__U61(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1)) -> c68(A__U61(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1)) -> c68(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1)) -> c68(A__U61(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1)) -> c68(A__U61(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1)) -> c68(A__U61(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U61(U61(z0, z1), x1)) -> c68(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(length(z0), x1)) -> c68(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(and(z0, z1), x1)) -> c68(A__U61(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1)) -> c68(A__U61(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1)) -> c68(A__U61(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U61(zeros, x1)) -> c68(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c68(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c68(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c69(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c69(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c69(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c69(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c69(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c69(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c69(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c69(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c69(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c69(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c69(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c69(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c69(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1))) -> c69(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(length(z0))) -> c69(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(and(z0, z1))) -> c69(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c69(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c69(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c69(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c69(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c69(MARK(s(z0))) MARK(and(U11(z0, z1), x1)) -> c70(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c70(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c70(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c70(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c70(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c70(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c70(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c70(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c70(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c70(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c70(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c70(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c70(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c70(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c70(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1), x1)) -> c70(A__AND(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(and(length(z0), x1)) -> c70(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(and(z0, z1), x1)) -> c70(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c70(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c70(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c70(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c70(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c70(MARK(s(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(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(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, U11(zeros, x1)) -> c26(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U61(tt, U11(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U61(tt, U11(U12(z0), x1)) -> c26(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U61(tt, U11(isNatList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U61(tt, U11(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U61(tt, U11(U22(z0), x1)) -> c26(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U61(tt, U11(isNat(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U61(tt, U11(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U61(tt, U11(U32(z0), x1)) -> c26(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U61(tt, U11(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U61(tt, U11(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U61(tt, U11(U43(z0), x1)) -> c26(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U61(tt, U11(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U61(tt, U11(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U61(tt, U11(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U61(tt, U11(U53(z0), x1)) -> c26(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U61(tt, U11(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__U61(mark(z0), z1), x1)), MARK(U11(U61(z0, z1), x1))) A__U61(tt, U11(length(z0), x1)) -> c26(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U61(tt, U11(and(z0, z1), x1)) -> c26(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U61(tt, U11(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U61(tt, U11(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U61(tt, U11(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U61(tt, U11(tt, x1)) -> c26(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U61(tt, U11(s(z0), x1)) -> c26(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1))) A__U61(tt, U11(0, x1)) -> c26(A__LENGTH(a__U11(0, x1))) A__U61(tt, U11(nil, x1)) -> c26(A__LENGTH(a__U11(nil, x1))) A__U61(tt, U12(zeros)) -> c26(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U61(tt, U12(U11(z0, z1))) -> c26(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U61(tt, U12(U12(z0))) -> c26(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U61(tt, U12(isNatList(z0))) -> c26(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U61(tt, U12(U21(z0, z1))) -> c26(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U61(tt, U12(U22(z0))) -> 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MARK(U41(isNat(z0), x1, x2))) A__U61(tt, U41(U31(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(U41(U31(z0, z1), x1, x2))) A__U61(tt, U41(U32(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U32(mark(z0)), x1, x2)), MARK(U41(U32(z0), x1, x2))) A__U61(tt, U41(U41(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2))) A__U61(tt, U41(U42(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U42(mark(z0), z1), x1, x2)), MARK(U41(U42(z0, z1), x1, x2))) A__U61(tt, U41(U43(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U43(mark(z0)), x1, x2)), MARK(U41(U43(z0), x1, x2))) A__U61(tt, U41(isNatIList(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatIList(z0), x1, x2)), MARK(U41(isNatIList(z0), x1, x2))) A__U61(tt, U41(U51(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U41(a__U51(mark(z0), z1, z2), x1, x2)), MARK(U41(U51(z0, z1, z2), x1, x2))) A__U61(tt, U41(U52(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U52(mark(z0), z1), x1, x2)), MARK(U41(U52(z0, z1), x1, x2))) A__U61(tt, U41(U53(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__U53(mark(z0)), x1, x2)), MARK(U41(U53(z0), x1, x2))) A__U61(tt, U41(U61(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__U61(mark(z0), z1), x1, x2)), MARK(U41(U61(z0, z1), x1, x2))) A__U61(tt, U41(length(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__length(mark(z0)), x1, x2)), MARK(U41(length(z0), x1, x2))) A__U61(tt, U41(and(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(a__and(mark(z0), z1), x1, x2)), MARK(U41(and(z0, z1), x1, x2))) A__U61(tt, U41(isNatIListKind(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatIListKind(z0), x1, x2)), MARK(U41(isNatIListKind(z0), x1, x2))) A__U61(tt, U41(isNatKind(z0), x1, x2)) -> c26(A__LENGTH(a__U41(a__isNatKind(z0), x1, x2)), MARK(U41(isNatKind(z0), x1, x2))) A__U61(tt, U41(cons(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U41(cons(mark(z0), z1), x1, x2)), MARK(U41(cons(z0, z1), x1, x2))) A__U61(tt, U41(tt, x1, x2)) -> c26(A__LENGTH(a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2))) A__U61(tt, U41(s(z0), x1, x2)) -> c26(A__LENGTH(a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2))) A__U61(tt, U41(x0, z1, z2)) -> c26(MARK(U41(x0, z1, z2))) A__U61(tt, U41(0, x1, x2)) -> c26(A__LENGTH(a__U41(0, x1, x2))) A__U61(tt, U41(nil, x1, x2)) -> c26(A__LENGTH(a__U41(nil, x1, x2))) A__U61(tt, U42(zeros, x1)) -> c26(A__LENGTH(a__U42(a__zeros, x1)), MARK(U42(zeros, x1))) A__U61(tt, U42(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U11(mark(z0), z1), x1)), MARK(U42(U11(z0, z1), x1))) A__U61(tt, U42(U12(z0), x1)) -> c26(A__LENGTH(a__U42(a__U12(mark(z0)), x1)), MARK(U42(U12(z0), x1))) A__U61(tt, U42(isNatList(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatList(z0), x1)), MARK(U42(isNatList(z0), x1))) A__U61(tt, U42(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U21(mark(z0), z1), x1)), MARK(U42(U21(z0, z1), x1))) A__U61(tt, U42(U22(z0), x1)) -> c26(A__LENGTH(a__U42(a__U22(mark(z0)), x1)), MARK(U42(U22(z0), x1))) A__U61(tt, U42(isNat(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNat(z0), x1)), MARK(U42(isNat(z0), x1))) A__U61(tt, U42(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U31(mark(z0), z1), x1)), MARK(U42(U31(z0, z1), x1))) A__U61(tt, U42(U32(z0), x1)) -> c26(A__LENGTH(a__U42(a__U32(mark(z0)), x1)), MARK(U42(U32(z0), x1))) A__U61(tt, U42(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U42(a__U41(mark(z0), z1, z2), x1)), MARK(U42(U41(z0, z1, z2), x1))) A__U61(tt, U42(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U42(mark(z0), z1), x1)), MARK(U42(U42(z0, z1), x1))) A__U61(tt, U42(U43(z0), x1)) -> c26(A__LENGTH(a__U42(a__U43(mark(z0)), x1)), MARK(U42(U43(z0), x1))) A__U61(tt, U42(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatIList(z0), x1)), MARK(U42(isNatIList(z0), x1))) A__U61(tt, U42(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U42(a__U51(mark(z0), z1, z2), x1)), MARK(U42(U51(z0, z1, z2), x1))) A__U61(tt, U42(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U52(mark(z0), z1), x1)), MARK(U42(U52(z0, z1), x1))) A__U61(tt, U42(U53(z0), x1)) -> c26(A__LENGTH(a__U42(a__U53(mark(z0)), x1)), MARK(U42(U53(z0), x1))) A__U61(tt, U42(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__U61(mark(z0), z1), x1)), MARK(U42(U61(z0, z1), x1))) A__U61(tt, U42(length(z0), x1)) -> c26(A__LENGTH(a__U42(a__length(mark(z0)), x1)), MARK(U42(length(z0), x1))) A__U61(tt, U42(and(z0, z1), x1)) -> c26(A__LENGTH(a__U42(a__and(mark(z0), z1), x1)), MARK(U42(and(z0, z1), x1))) A__U61(tt, U42(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatIListKind(z0), x1)), MARK(U42(isNatIListKind(z0), x1))) A__U61(tt, U42(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U42(a__isNatKind(z0), x1)), MARK(U42(isNatKind(z0), x1))) A__U61(tt, U42(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U42(cons(mark(z0), z1), x1)), MARK(U42(cons(z0, z1), x1))) A__U61(tt, U42(tt, x1)) -> c26(A__LENGTH(a__U42(tt, x1)), MARK(U42(tt, x1))) A__U61(tt, U42(s(z0), x1)) -> c26(A__LENGTH(a__U42(s(mark(z0)), x1)), MARK(U42(s(z0), x1))) A__U61(tt, U42(x0, z1)) -> c26(MARK(U42(x0, z1))) A__U61(tt, U42(0, x1)) -> c26(A__LENGTH(a__U42(0, x1))) A__U61(tt, U42(nil, x1)) -> c26(A__LENGTH(a__U42(nil, x1))) A__U61(tt, U43(zeros)) -> c26(A__LENGTH(a__U43(a__zeros)), MARK(U43(zeros))) A__U61(tt, U43(U11(z0, z1))) -> c26(A__LENGTH(a__U43(a__U11(mark(z0), z1))), MARK(U43(U11(z0, z1)))) A__U61(tt, U43(U12(z0))) -> c26(A__LENGTH(a__U43(a__U12(mark(z0)))), MARK(U43(U12(z0)))) A__U61(tt, U43(isNatList(z0))) -> c26(A__LENGTH(a__U43(a__isNatList(z0))), MARK(U43(isNatList(z0)))) A__U61(tt, U43(U21(z0, z1))) -> c26(A__LENGTH(a__U43(a__U21(mark(z0), z1))), MARK(U43(U21(z0, z1)))) A__U61(tt, U43(U22(z0))) -> c26(A__LENGTH(a__U43(a__U22(mark(z0)))), MARK(U43(U22(z0)))) A__U61(tt, U43(isNat(z0))) -> c26(A__LENGTH(a__U43(a__isNat(z0))), MARK(U43(isNat(z0)))) A__U61(tt, U43(U31(z0, z1))) -> c26(A__LENGTH(a__U43(a__U31(mark(z0), z1))), MARK(U43(U31(z0, z1)))) A__U61(tt, U43(U32(z0))) -> c26(A__LENGTH(a__U43(a__U32(mark(z0)))), MARK(U43(U32(z0)))) A__U61(tt, U43(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U43(a__U41(mark(z0), z1, z2))), MARK(U43(U41(z0, z1, z2)))) A__U61(tt, U43(U42(z0, z1))) -> c26(A__LENGTH(a__U43(a__U42(mark(z0), z1))), MARK(U43(U42(z0, z1)))) A__U61(tt, U43(U43(z0))) -> c26(A__LENGTH(a__U43(a__U43(mark(z0)))), MARK(U43(U43(z0)))) A__U61(tt, U43(isNatIList(z0))) -> c26(A__LENGTH(a__U43(a__isNatIList(z0))), MARK(U43(isNatIList(z0)))) A__U61(tt, U43(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U43(a__U51(mark(z0), z1, z2))), MARK(U43(U51(z0, z1, z2)))) A__U61(tt, U43(U52(z0, z1))) -> c26(A__LENGTH(a__U43(a__U52(mark(z0), z1))), MARK(U43(U52(z0, z1)))) A__U61(tt, U43(U53(z0))) -> c26(A__LENGTH(a__U43(a__U53(mark(z0)))), MARK(U43(U53(z0)))) A__U61(tt, U43(U61(z0, z1))) -> c26(A__LENGTH(a__U43(a__U61(mark(z0), z1))), MARK(U43(U61(z0, z1)))) A__U61(tt, U43(length(z0))) -> c26(A__LENGTH(a__U43(a__length(mark(z0)))), MARK(U43(length(z0)))) A__U61(tt, U43(and(z0, z1))) -> c26(A__LENGTH(a__U43(a__and(mark(z0), z1))), MARK(U43(and(z0, z1)))) A__U61(tt, U43(isNatIListKind(z0))) -> c26(A__LENGTH(a__U43(a__isNatIListKind(z0))), MARK(U43(isNatIListKind(z0)))) A__U61(tt, U43(isNatKind(z0))) -> c26(A__LENGTH(a__U43(a__isNatKind(z0))), MARK(U43(isNatKind(z0)))) A__U61(tt, U43(cons(z0, z1))) -> c26(A__LENGTH(a__U43(cons(mark(z0), z1))), MARK(U43(cons(z0, z1)))) A__U61(tt, U43(0)) -> c26(A__LENGTH(a__U43(0)), MARK(U43(0))) A__U61(tt, U43(tt)) -> c26(A__LENGTH(a__U43(tt)), MARK(U43(tt))) A__U61(tt, U43(s(z0))) -> c26(A__LENGTH(a__U43(s(mark(z0)))), MARK(U43(s(z0)))) A__U61(tt, U43(nil)) -> c26(A__LENGTH(a__U43(nil)), MARK(U43(nil))) A__U61(tt, U43(x0)) -> c26(MARK(U43(x0))) A__U61(tt, isNatIList(z0)) -> c26(A__LENGTH(a__U31(a__isNatIListKind(z0), z0)), MARK(isNatIList(z0))) A__U61(tt, isNatIList(cons(z0, z1))) -> c26(A__LENGTH(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatIList(cons(z0, z1)))) A__U61(tt, isNatIList(zeros)) -> c26(MARK(isNatIList(zeros))) A__U61(tt, isNatIList(z0)) -> c26(MARK(isNatIList(z0))) A__U61(tt, U51(zeros, x1, x2)) -> c26(A__LENGTH(a__U51(a__zeros, x1, x2)), MARK(U51(zeros, x1, x2))) A__U61(tt, U51(U11(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U11(mark(z0), z1), x1, x2)), MARK(U51(U11(z0, z1), x1, x2))) A__U61(tt, U51(U12(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U12(mark(z0)), x1, x2)), MARK(U51(U12(z0), x1, x2))) A__U61(tt, U51(isNatList(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatList(z0), x1, x2)), MARK(U51(isNatList(z0), x1, x2))) A__U61(tt, U51(U21(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U21(mark(z0), z1), x1, x2)), MARK(U51(U21(z0, z1), x1, x2))) A__U61(tt, U51(U22(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U22(mark(z0)), x1, x2)), MARK(U51(U22(z0), x1, x2))) A__U61(tt, U51(isNat(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNat(z0), x1, x2)), MARK(U51(isNat(z0), x1, x2))) A__U61(tt, U51(U31(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U31(mark(z0), z1), x1, x2)), MARK(U51(U31(z0, z1), x1, x2))) A__U61(tt, U51(U32(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U32(mark(z0)), x1, x2)), MARK(U51(U32(z0), x1, x2))) A__U61(tt, U51(U41(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U51(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U51(U41(z0, z1, z2), x1, x2))) A__U61(tt, U51(U42(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U42(mark(z0), z1), x1, x2)), MARK(U51(U42(z0, z1), x1, x2))) A__U61(tt, U51(U43(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U43(mark(z0)), x1, x2)), MARK(U51(U43(z0), x1, x2))) A__U61(tt, U51(isNatIList(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatIList(z0), x1, x2)), MARK(U51(isNatIList(z0), x1, x2))) A__U61(tt, U51(U51(z0, z1, z2), x1, x2)) -> c26(A__LENGTH(a__U51(a__U51(mark(z0), z1, z2), x1, x2)), MARK(U51(U51(z0, z1, z2), x1, x2))) A__U61(tt, U51(U52(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U52(mark(z0), z1), x1, x2)), MARK(U51(U52(z0, z1), x1, x2))) A__U61(tt, U51(U53(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__U53(mark(z0)), x1, x2)), MARK(U51(U53(z0), x1, x2))) A__U61(tt, U51(U61(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__U61(mark(z0), z1), x1, x2)), MARK(U51(U61(z0, z1), x1, x2))) A__U61(tt, U51(length(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__length(mark(z0)), x1, x2)), MARK(U51(length(z0), x1, x2))) A__U61(tt, U51(and(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(a__and(mark(z0), z1), x1, x2)), MARK(U51(and(z0, z1), x1, x2))) A__U61(tt, U51(isNatIListKind(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatIListKind(z0), x1, x2)), MARK(U51(isNatIListKind(z0), x1, x2))) A__U61(tt, U51(isNatKind(z0), x1, x2)) -> c26(A__LENGTH(a__U51(a__isNatKind(z0), x1, x2)), MARK(U51(isNatKind(z0), x1, x2))) A__U61(tt, U51(cons(z0, z1), x1, x2)) -> c26(A__LENGTH(a__U51(cons(mark(z0), z1), x1, x2)), MARK(U51(cons(z0, z1), x1, x2))) A__U61(tt, U51(tt, x1, x2)) -> c26(A__LENGTH(a__U51(tt, x1, x2)), MARK(U51(tt, x1, x2))) A__U61(tt, U51(s(z0), x1, x2)) -> c26(A__LENGTH(a__U51(s(mark(z0)), x1, x2)), MARK(U51(s(z0), x1, x2))) A__U61(tt, U51(x0, z1, z2)) -> c26(MARK(U51(x0, z1, z2))) A__U61(tt, U51(0, x1, x2)) -> c26(A__LENGTH(a__U51(0, x1, x2))) A__U61(tt, U51(nil, x1, x2)) -> c26(A__LENGTH(a__U51(nil, x1, x2))) A__U61(tt, U52(zeros, x1)) -> c26(A__LENGTH(a__U52(a__zeros, x1)), MARK(U52(zeros, x1))) A__U61(tt, U52(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U11(mark(z0), z1), x1)), MARK(U52(U11(z0, z1), x1))) A__U61(tt, U52(U12(z0), x1)) -> c26(A__LENGTH(a__U52(a__U12(mark(z0)), x1)), MARK(U52(U12(z0), x1))) A__U61(tt, U52(isNatList(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatList(z0), x1)), MARK(U52(isNatList(z0), x1))) A__U61(tt, U52(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U21(mark(z0), z1), x1)), MARK(U52(U21(z0, z1), x1))) A__U61(tt, U52(U22(z0), x1)) -> c26(A__LENGTH(a__U52(a__U22(mark(z0)), x1)), MARK(U52(U22(z0), x1))) A__U61(tt, U52(isNat(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNat(z0), x1)), MARK(U52(isNat(z0), x1))) A__U61(tt, U52(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U31(mark(z0), z1), x1)), MARK(U52(U31(z0, z1), x1))) A__U61(tt, U52(U32(z0), x1)) -> c26(A__LENGTH(a__U52(a__U32(mark(z0)), x1)), MARK(U52(U32(z0), x1))) A__U61(tt, U52(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U52(a__U41(mark(z0), z1, z2), x1)), MARK(U52(U41(z0, z1, z2), x1))) A__U61(tt, U52(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U42(mark(z0), z1), x1)), MARK(U52(U42(z0, z1), x1))) A__U61(tt, U52(U43(z0), x1)) -> c26(A__LENGTH(a__U52(a__U43(mark(z0)), x1)), MARK(U52(U43(z0), x1))) A__U61(tt, U52(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatIList(z0), x1)), MARK(U52(isNatIList(z0), x1))) A__U61(tt, U52(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U52(a__U51(mark(z0), z1, z2), x1)), MARK(U52(U51(z0, z1, z2), x1))) A__U61(tt, U52(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U52(mark(z0), z1), x1)), MARK(U52(U52(z0, z1), x1))) A__U61(tt, U52(U53(z0), x1)) -> c26(A__LENGTH(a__U52(a__U53(mark(z0)), x1)), MARK(U52(U53(z0), x1))) A__U61(tt, U52(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__U61(mark(z0), z1), x1)), MARK(U52(U61(z0, z1), x1))) A__U61(tt, U52(length(z0), x1)) -> c26(A__LENGTH(a__U52(a__length(mark(z0)), x1)), MARK(U52(length(z0), x1))) A__U61(tt, U52(and(z0, z1), x1)) -> c26(A__LENGTH(a__U52(a__and(mark(z0), z1), x1)), MARK(U52(and(z0, z1), x1))) A__U61(tt, U52(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatIListKind(z0), x1)), MARK(U52(isNatIListKind(z0), x1))) A__U61(tt, U52(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U52(a__isNatKind(z0), x1)), MARK(U52(isNatKind(z0), x1))) A__U61(tt, U52(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U52(cons(mark(z0), z1), x1)), MARK(U52(cons(z0, z1), x1))) A__U61(tt, U52(tt, x1)) -> c26(A__LENGTH(a__U52(tt, x1)), MARK(U52(tt, x1))) A__U61(tt, U52(s(z0), x1)) -> c26(A__LENGTH(a__U52(s(mark(z0)), x1)), MARK(U52(s(z0), x1))) A__U61(tt, U52(x0, z1)) -> c26(MARK(U52(x0, z1))) A__U61(tt, U52(0, x1)) -> c26(A__LENGTH(a__U52(0, x1))) A__U61(tt, U52(nil, x1)) -> c26(A__LENGTH(a__U52(nil, x1))) A__U61(tt, U53(zeros)) -> c26(A__LENGTH(a__U53(a__zeros)), MARK(U53(zeros))) A__U61(tt, U53(U11(z0, z1))) -> c26(A__LENGTH(a__U53(a__U11(mark(z0), z1))), MARK(U53(U11(z0, z1)))) A__U61(tt, U53(U12(z0))) -> c26(A__LENGTH(a__U53(a__U12(mark(z0)))), MARK(U53(U12(z0)))) A__U61(tt, U53(isNatList(z0))) -> c26(A__LENGTH(a__U53(a__isNatList(z0))), MARK(U53(isNatList(z0)))) A__U61(tt, U53(U21(z0, z1))) -> c26(A__LENGTH(a__U53(a__U21(mark(z0), z1))), MARK(U53(U21(z0, z1)))) A__U61(tt, U53(U22(z0))) -> c26(A__LENGTH(a__U53(a__U22(mark(z0)))), MARK(U53(U22(z0)))) A__U61(tt, U53(isNat(z0))) -> c26(A__LENGTH(a__U53(a__isNat(z0))), MARK(U53(isNat(z0)))) A__U61(tt, U53(U31(z0, z1))) -> c26(A__LENGTH(a__U53(a__U31(mark(z0), z1))), MARK(U53(U31(z0, z1)))) A__U61(tt, U53(U32(z0))) -> c26(A__LENGTH(a__U53(a__U32(mark(z0)))), MARK(U53(U32(z0)))) A__U61(tt, U53(U41(z0, z1, z2))) -> c26(A__LENGTH(a__U53(a__U41(mark(z0), z1, z2))), MARK(U53(U41(z0, z1, z2)))) A__U61(tt, U53(U42(z0, z1))) -> c26(A__LENGTH(a__U53(a__U42(mark(z0), z1))), MARK(U53(U42(z0, z1)))) A__U61(tt, U53(U43(z0))) -> c26(A__LENGTH(a__U53(a__U43(mark(z0)))), MARK(U53(U43(z0)))) A__U61(tt, U53(isNatIList(z0))) -> c26(A__LENGTH(a__U53(a__isNatIList(z0))), MARK(U53(isNatIList(z0)))) A__U61(tt, U53(U51(z0, z1, z2))) -> c26(A__LENGTH(a__U53(a__U51(mark(z0), z1, z2))), MARK(U53(U51(z0, z1, z2)))) A__U61(tt, U53(U52(z0, z1))) -> c26(A__LENGTH(a__U53(a__U52(mark(z0), z1))), MARK(U53(U52(z0, z1)))) A__U61(tt, U53(U53(z0))) -> c26(A__LENGTH(a__U53(a__U53(mark(z0)))), MARK(U53(U53(z0)))) A__U61(tt, U53(U61(z0, z1))) -> c26(A__LENGTH(a__U53(a__U61(mark(z0), z1))), MARK(U53(U61(z0, z1)))) A__U61(tt, U53(length(z0))) -> c26(A__LENGTH(a__U53(a__length(mark(z0)))), MARK(U53(length(z0)))) A__U61(tt, U53(and(z0, z1))) -> c26(A__LENGTH(a__U53(a__and(mark(z0), z1))), MARK(U53(and(z0, z1)))) A__U61(tt, U53(isNatIListKind(z0))) -> c26(A__LENGTH(a__U53(a__isNatIListKind(z0))), MARK(U53(isNatIListKind(z0)))) A__U61(tt, U53(isNatKind(z0))) -> c26(A__LENGTH(a__U53(a__isNatKind(z0))), MARK(U53(isNatKind(z0)))) A__U61(tt, U53(cons(z0, z1))) -> c26(A__LENGTH(a__U53(cons(mark(z0), z1))), MARK(U53(cons(z0, z1)))) A__U61(tt, U53(0)) -> c26(A__LENGTH(a__U53(0)), MARK(U53(0))) A__U61(tt, U53(tt)) -> c26(A__LENGTH(a__U53(tt)), MARK(U53(tt))) A__U61(tt, U53(s(z0))) -> c26(A__LENGTH(a__U53(s(mark(z0)))), MARK(U53(s(z0)))) A__U61(tt, U53(nil)) -> c26(A__LENGTH(a__U53(nil)), MARK(U53(nil))) A__U61(tt, U53(x0)) -> c26(MARK(U53(x0))) A__U61(tt, U61(zeros, x1)) -> c26(A__LENGTH(a__U61(a__zeros, x1)), MARK(U61(zeros, x1))) A__U61(tt, U61(U11(z0, z1), x1)) -> c26(A__LENGTH(a__U61(a__U11(mark(z0), z1), x1)), MARK(U61(U11(z0, z1), x1))) A__U61(tt, U61(U12(z0), x1)) -> c26(A__LENGTH(a__U61(a__U12(mark(z0)), x1)), MARK(U61(U12(z0), x1))) A__U61(tt, U61(isNatList(z0), x1)) -> c26(A__LENGTH(a__U61(a__isNatList(z0), x1)), MARK(U61(isNatList(z0), x1))) A__U61(tt, U61(U21(z0, z1), x1)) -> c26(A__LENGTH(a__U61(a__U21(mark(z0), z1), x1)), MARK(U61(U21(z0, z1), x1))) A__U61(tt, U61(U22(z0), x1)) -> c26(A__LENGTH(a__U61(a__U22(mark(z0)), x1)), MARK(U61(U22(z0), x1))) A__U61(tt, U61(isNat(z0), x1)) -> c26(A__LENGTH(a__U61(a__isNat(z0), x1)), MARK(U61(isNat(z0), x1))) A__U61(tt, U61(U31(z0, z1), x1)) -> c26(A__LENGTH(a__U61(a__U31(mark(z0), z1), x1)), MARK(U61(U31(z0, z1), x1))) A__U61(tt, U61(U32(z0), x1)) -> c26(A__LENGTH(a__U61(a__U32(mark(z0)), x1)), MARK(U61(U32(z0), x1))) A__U61(tt, U61(U41(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U61(a__U41(mark(z0), z1, z2), x1)), MARK(U61(U41(z0, z1, z2), x1))) A__U61(tt, U61(U42(z0, z1), x1)) -> c26(A__LENGTH(a__U61(a__U42(mark(z0), z1), x1)), MARK(U61(U42(z0, z1), x1))) A__U61(tt, U61(U43(z0), x1)) -> c26(A__LENGTH(a__U61(a__U43(mark(z0)), x1)), MARK(U61(U43(z0), x1))) A__U61(tt, U61(isNatIList(z0), x1)) -> c26(A__LENGTH(a__U61(a__isNatIList(z0), x1)), MARK(U61(isNatIList(z0), x1))) A__U61(tt, U61(U51(z0, z1, z2), x1)) -> c26(A__LENGTH(a__U61(a__U51(mark(z0), z1, z2), x1)), MARK(U61(U51(z0, z1, z2), x1))) A__U61(tt, U61(U52(z0, z1), x1)) -> c26(A__LENGTH(a__U61(a__U52(mark(z0), z1), x1)), MARK(U61(U52(z0, z1), x1))) A__U61(tt, U61(U53(z0), x1)) -> c26(A__LENGTH(a__U61(a__U53(mark(z0)), x1)), MARK(U61(U53(z0), x1))) A__U61(tt, U61(U61(z0, z1), x1)) -> c26(A__LENGTH(a__U61(a__U61(mark(z0), z1), x1)), MARK(U61(U61(z0, z1), x1))) A__U61(tt, U61(length(z0), x1)) -> c26(A__LENGTH(a__U61(a__length(mark(z0)), x1)), MARK(U61(length(z0), x1))) A__U61(tt, U61(and(z0, z1), x1)) -> c26(A__LENGTH(a__U61(a__and(mark(z0), z1), x1)), MARK(U61(and(z0, z1), x1))) A__U61(tt, U61(isNatIListKind(z0), x1)) -> c26(A__LENGTH(a__U61(a__isNatIListKind(z0), x1)), MARK(U61(isNatIListKind(z0), x1))) A__U61(tt, U61(isNatKind(z0), x1)) -> c26(A__LENGTH(a__U61(a__isNatKind(z0), x1)), MARK(U61(isNatKind(z0), x1))) A__U61(tt, U61(cons(z0, z1), x1)) -> c26(A__LENGTH(a__U61(cons(mark(z0), z1), x1)), MARK(U61(cons(z0, z1), x1))) A__U61(tt, U61(tt, x1)) -> c26(A__LENGTH(a__U61(tt, x1)), MARK(U61(tt, x1))) A__U61(tt, U61(s(z0), x1)) -> c26(A__LENGTH(a__U61(s(mark(z0)), x1)), MARK(U61(s(z0), x1))) A__U61(tt, U61(x0, z1)) -> c26(MARK(U61(x0, z1))) A__U61(tt, U61(0, x1)) -> c26(A__LENGTH(a__U61(0, x1))) A__U61(tt, U61(nil, x1)) -> c26(A__LENGTH(a__U61(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_2, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U41_3, A__U51_3, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c28_1, c43_1, c44_1, c55_1, c58_1, c64_1, c71_1, c72_1, c73_1, c76_1, c2_1, c6_1, c10_1, c16_1, c22_1, c54_1, c57_1, c60_1, c63_1, c67_1, c14_1, c20_1, c26_2, c26_1, c31_2, c31_1, c32_2, c32_1, c34_2, c34_1, c36_3, c36_2, c40_2, c40_1, c47_3, c47_2, c50_4, c50_3, c50_2, c53_2, c53_1, c56_2, c56_1, c59_2, c59_1, c61_2, c61_1, c62_2, c62_1, c65_2, c65_1, c66_2, c66_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c14_2, c20_2