KILLED
proof of input_ERE6CVqpeu.trs
# AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished


The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).

(0) CpxTRS
(1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxTRS
(3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(4) CpxTRS
(5) CpxTrsToCdtProof [UPPER BOUND(ID), 69 ms]
(6) CdtProblem
    (7) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) CpxRelTRS
    (9) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
    (10) TRS for Loop Detection
    (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (12) CpxRelTRS
        (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
        (14) typed CpxTrs
        (15) OrderProof [LOWER BOUND(ID), 76 ms]
        (16) typed CpxTrs
(17) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(18) CdtProblem
    (19) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CdtProblem
    (21) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (22) CdtProblem
    (23) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (24) CpxRelTRS
        (25) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
        (26) CpxTRS
        (27) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
        (28) CpxWeightedTrs
            (29) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
            (30) CpxTypedWeightedTrs
            (31) CompletionProof [UPPER BOUND(ID), 0 ms]
            (32) CpxTypedWeightedCompleteTrs
                (33) NarrowingProof [BOTH BOUNDS(ID, ID), 699 ms]
                (34) CpxTypedWeightedCompleteTrs
                (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 6 ms]
                (36) CpxRNTS
                (37) InliningProof [UPPER BOUND(ID), 1260 ms]
                (38) CpxRNTS
                (39) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
                (40) CpxRNTS
            (41) CompletionProof [UPPER BOUND(ID), 12 ms]
            (42) CpxTypedWeightedCompleteTrs
                (43) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
                (44) CpxRNTS
    (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (46) CdtProblem
        (47) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (50) CdtProblem
        (51) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (54) CdtProblem
        (55) CdtLeafRemovalProof [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), 0 ms]
        (68) CdtProblem
        (69) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (70) CdtProblem
        (71) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (72) CdtProblem
        (73) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (74) CdtProblem
        (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (76) CdtProblem
        (77) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (78) CdtProblem
        (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 15 ms]
        (80) CdtProblem
        (81) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (82) CdtProblem
        (83) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 28 ms]
        (84) CdtProblem
        (85) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (86) CdtProblem
        (87) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (88) CdtProblem
        (89) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (90) CdtProblem
        (91) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (92) CdtProblem
        (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 21 ms]
        (94) CdtProblem
        (95) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (96) CdtProblem
        (97) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (98) CdtProblem
        (99) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 39 ms]
        (100) CdtProblem
        (101) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (102) CdtProblem
        (103) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (104) CdtProblem
        (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 28 ms]
        (106) CdtProblem
        (107) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (108) CdtProblem
        (109) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (110) CdtProblem
        (111) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 46 ms]
        (112) CdtProblem
        (113) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (114) CdtProblem
        (115) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (116) CdtProblem
        (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 38 ms]
        (118) CdtProblem
        (119) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (120) CdtProblem
        (121) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (122) CdtProblem
        (123) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 33 ms]
        (124) CdtProblem
        (125) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (126) CdtProblem
        (127) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (128) CdtProblem
        (129) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 49 ms]
        (130) CdtProblem
        (131) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (132) CdtProblem
        (133) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (134) CdtProblem
        (135) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 91 ms]
        (136) CdtProblem
        (137) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (138) CdtProblem
        (139) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (140) CdtProblem
        (141) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 77 ms]
        (142) CdtProblem
        (143) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 4 ms]
        (144) CdtProblem
        (145) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 7 ms]
        (146) CdtProblem
        (147) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 51 ms]
        (148) CdtProblem
        (149) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (150) CdtProblem
        (151) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (152) CdtProblem
        (153) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (154) CdtProblem
        (155) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 26 ms]
        (156) CdtProblem
        (157) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (158) CdtProblem
        (159) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 7 ms]
        (160) CdtProblem
        (161) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (162) CdtProblem
        (163) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 45 ms]
        (164) CdtProblem
        (165) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (166) CdtProblem
        (167) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 30 ms]
        (168) CdtProblem
        (169) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (170) CdtProblem
        (171) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (172) CdtProblem
        (173) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (174) CdtProblem
        (175) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 69 ms]
        (176) CdtProblem
        (177) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (178) CdtProblem
        (179) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 23 ms]
        (180) CdtProblem
        (181) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (182) CdtProblem
        (183) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 36 ms]
        (184) CdtProblem
        (185) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (186) CdtProblem
        (187) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 39 ms]
        (188) CdtProblem
        (189) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (190) CdtProblem
        (191) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 22 ms]
        (192) CdtProblem
        (193) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (194) CdtProblem
        (195) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 50 ms]
        (196) CdtProblem
        (197) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (198) CdtProblem
        (199) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 43 ms]
        (200) CdtProblem
        (201) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (202) CdtProblem
        (203) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 49 ms]
        (204) CdtProblem
        (205) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (206) CdtProblem
        (207) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 42 ms]
        (208) CdtProblem
        (209) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (210) CdtProblem
        (211) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (212) CdtProblem
        (213) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (214) CdtProblem
        (215) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 24 ms]
        (216) CdtProblem
        (217) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (218) CdtProblem
        (219) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 28 ms]
        (220) CdtProblem
        (221) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (222) CdtProblem
        (223) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 54 ms]
        (224) CdtProblem
        (225) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 9 ms]
        (226) CdtProblem
(227) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms]
(228) CpxWeightedTrs
    (229) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (230) CpxTypedWeightedTrs
    (231) CompletionProof [UPPER BOUND(ID), 0 ms]
    (232) CpxTypedWeightedCompleteTrs
        (233) NarrowingProof [BOTH BOUNDS(ID, ID), 169 ms]
        (234) CpxTypedWeightedCompleteTrs
        (235) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (236) CpxRNTS
        (237) InliningProof [UPPER BOUND(ID), 622 ms]
        (238) CpxRNTS
        (239) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (240) CpxRNTS
    (241) CompletionProof [UPPER BOUND(ID), 0 ms]
    (242) CpxTypedWeightedCompleteTrs
        (243) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 20 ms]
        (244) CpxRNTS


----------------------------------------

(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) CpxTrsToCdtProof (UPPER BOUND(ID))
Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT
----------------------------------------

(6)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0) -> 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


----------------------------------------

(7) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID))
Converted S to standard rules, and D \ S as well as R to relative rules.
----------------------------------------

(8)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   A__ZEROS -> c
   A__ZEROS -> c1
   A__U11(tt, z0) -> c2(A__U12(a__isNatList(z0)), A__ISNATLIST(z0))
   A__U11(z0, z1) -> c3
   A__U12(tt) -> c4
   A__U12(z0) -> c5
   A__U21(tt, z0) -> c6(A__U22(a__isNat(z0)), A__ISNAT(z0))
   A__U21(z0, z1) -> c7
   A__U22(tt) -> c8
   A__U22(z0) -> c9
   A__U31(tt, z0) -> c10(A__U32(a__isNatList(z0)), A__ISNATLIST(z0))
   A__U31(z0, z1) -> c11
   A__U32(tt) -> c12
   A__U32(z0) -> c13
   A__U41(tt, z0, z1) -> c14(A__U42(a__isNat(z0), z1), A__ISNAT(z0))
   A__U41(z0, z1, z2) -> c15
   A__U42(tt, z0) -> c16(A__U43(a__isNatIList(z0)), A__ISNATILIST(z0))
   A__U42(z0, z1) -> c17
   A__U43(tt) -> c18
   A__U43(z0) -> c19
   A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0))
   A__U51(z0, z1, z2) -> c21
   A__U52(tt, z0) -> c22(A__U53(a__isNatList(z0)), A__ISNATLIST(z0))
   A__U52(z0, z1) -> c23
   A__U53(tt) -> c24
   A__U53(z0) -> c25
   A__U61(tt, z0) -> 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

The (relative) TRS S consists of the following rules:

   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0) -> 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

Rewrite Strategy: INNERMOST
----------------------------------------

(9) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
Transformed a relative TRS into a decreasing-loop problem.
----------------------------------------

(10)
Obligation:
Analyzing the following TRS for decreasing loops:

The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   A__ZEROS -> c
   A__ZEROS -> c1
   A__U11(tt, z0) -> c2(A__U12(a__isNatList(z0)), A__ISNATLIST(z0))
   A__U11(z0, z1) -> c3
   A__U12(tt) -> c4
   A__U12(z0) -> c5
   A__U21(tt, z0) -> c6(A__U22(a__isNat(z0)), A__ISNAT(z0))
   A__U21(z0, z1) -> c7
   A__U22(tt) -> c8
   A__U22(z0) -> c9
   A__U31(tt, z0) -> c10(A__U32(a__isNatList(z0)), A__ISNATLIST(z0))
   A__U31(z0, z1) -> c11
   A__U32(tt) -> c12
   A__U32(z0) -> c13
   A__U41(tt, z0, z1) -> c14(A__U42(a__isNat(z0), z1), A__ISNAT(z0))
   A__U41(z0, z1, z2) -> c15
   A__U42(tt, z0) -> c16(A__U43(a__isNatIList(z0)), A__ISNATILIST(z0))
   A__U42(z0, z1) -> c17
   A__U43(tt) -> c18
   A__U43(z0) -> c19
   A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0))
   A__U51(z0, z1, z2) -> c21
   A__U52(tt, z0) -> c22(A__U53(a__isNatList(z0)), A__ISNATLIST(z0))
   A__U52(z0, z1) -> c23
   A__U53(tt) -> c24
   A__U53(z0) -> c25
   A__U61(tt, z0) -> 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

The (relative) TRS S consists of the following rules:

   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0) -> 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

Rewrite Strategy: INNERMOST
----------------------------------------

(11) RenamingProof (BOTH BOUNDS(ID, ID))
Renamed function symbols to avoid clashes with predefined symbol.
----------------------------------------

(12)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   A__ZEROS -> c
   A__ZEROS -> c1
   A__U11(tt, z0) -> c2(A__U12(a__isNatList(z0)), A__ISNATLIST(z0))
   A__U11(z0, z1) -> c3
   A__U12(tt) -> c4
   A__U12(z0) -> c5
   A__U21(tt, z0) -> c6(A__U22(a__isNat(z0)), A__ISNAT(z0))
   A__U21(z0, z1) -> c7
   A__U22(tt) -> c8
   A__U22(z0) -> c9
   A__U31(tt, z0) -> c10(A__U32(a__isNatList(z0)), A__ISNATLIST(z0))
   A__U31(z0, z1) -> c11
   A__U32(tt) -> c12
   A__U32(z0) -> c13
   A__U41(tt, z0, z1) -> c14(A__U42(a__isNat(z0), z1), A__ISNAT(z0))
   A__U41(z0, z1, z2) -> c15
   A__U42(tt, z0) -> c16(A__U43(a__isNatIList(z0)), A__ISNATILIST(z0))
   A__U42(z0, z1) -> c17
   A__U43(tt) -> c18
   A__U43(z0) -> c19
   A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0))
   A__U51(z0, z1, z2) -> c21
   A__U52(tt, z0) -> c22(A__U53(a__isNatList(z0)), A__ISNATLIST(z0))
   A__U52(z0, z1) -> c23
   A__U53(tt) -> c24
   A__U53(z0) -> c25
   A__U61(tt, z0) -> 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

The (relative) TRS S consists of the following rules:

   a__zeros -> cons(0', zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0) -> 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

Rewrite Strategy: INNERMOST
----------------------------------------

(13) TypeInferenceProof (BOTH BOUNDS(ID, ID))
Inferred types.
----------------------------------------

(14)
Obligation:
Innermost TRS:
Rules:
A__ZEROS -> c
A__ZEROS -> c1
A__U11(tt, z0) -> c2(A__U12(a__isNatList(z0)), A__ISNATLIST(z0))
A__U11(z0, z1) -> c3
A__U12(tt) -> c4
A__U12(z0) -> c5
A__U21(tt, z0) -> c6(A__U22(a__isNat(z0)), A__ISNAT(z0))
A__U21(z0, z1) -> c7
A__U22(tt) -> c8
A__U22(z0) -> c9
A__U31(tt, z0) -> c10(A__U32(a__isNatList(z0)), A__ISNATLIST(z0))
A__U31(z0, z1) -> c11
A__U32(tt) -> c12
A__U32(z0) -> c13
A__U41(tt, z0, z1) -> c14(A__U42(a__isNat(z0), z1), A__ISNAT(z0))
A__U41(z0, z1, z2) -> c15
A__U42(tt, z0) -> c16(A__U43(a__isNatIList(z0)), A__ISNATILIST(z0))
A__U42(z0, z1) -> c17
A__U43(tt) -> c18
A__U43(z0) -> c19
A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0))
A__U51(z0, z1, z2) -> c21
A__U52(tt, z0) -> c22(A__U53(a__isNatList(z0)), A__ISNATLIST(z0))
A__U52(z0, z1) -> c23
A__U53(tt) -> c24
A__U53(z0) -> c25
A__U61(tt, z0) -> 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
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

Types:
A__ZEROS :: c:c1
c :: c:c1
c1 :: c:c1
A__U11 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> c2:c3
tt :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c2 :: c4:c5 -> c46:c47:c48 -> c2:c3
A__U12 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> c4:c5
a__isNatList :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
A__ISNATLIST :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> c46:c47:c48
c3 :: c2:c3
c4 :: c4:c5
c5 :: c4:c5
A__U21 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> c6:c7
c6 :: c8:c9 -> c30:c31:c32:c33 -> c6:c7
A__U22 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> c8:c9
a__isNat :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
A__ISNAT :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> c30:c31:c32:c33
c7 :: c6:c7
c8 :: c8:c9
c9 :: c8:c9
A__U31 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> c10:c11
c10 :: c12:c13 -> c46:c47:c48 -> c10:c11
A__U32 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> c12:c13
c11 :: c10:c11
c12 :: c12:c13
c13 :: c12:c13
A__U41 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> c14:c15
c14 :: c16:c17 -> c30:c31:c32:c33 -> c14:c15
A__U42 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> c16:c17
c15 :: c14:c15
c16 :: c18:c19 -> c34:c35:c36:c37 -> c16:c17
A__U43 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> c18:c19
a__isNatIList :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
A__ISNATILIST :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> c34:c35:c36:c37
c17 :: c16:c17
c18 :: c18:c19
c19 :: c18:c19
A__U51 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> c20:c21
c20 :: c22:c23 -> c30:c31:c32:c33 -> c20:c21
A__U52 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> c22:c23
c21 :: c20:c21
c22 :: c24:c25 -> c46:c47:c48 -> c22:c23
A__U53 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> c24:c25
c23 :: c22:c23
c24 :: c24:c25
c25 :: c24:c25
A__U61 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> c26:c27
c26 :: c49:c50:c51 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77 -> c26:c27
A__LENGTH :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> c49:c50:c51
mark :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
MARK :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
c27 :: c26:c27
A__AND :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> c28:c29
c28 :: c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77 -> c28:c29
c29 :: c28:c29
0' :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c30 :: c30:c31:c32:c33
length :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c31 :: c2:c3 -> c38:c39:c40:c41 -> c30:c31:c32:c33
a__isNatIListKind :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
A__ISNATILISTKIND :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> c38:c39:c40:c41
s :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c32 :: c6:c7 -> c42:c43:c44:c45 -> c30:c31:c32:c33
a__isNatKind :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
A__ISNATKIND :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> c42:c43:c44:c45
c33 :: c30:c31:c32:c33
c34 :: c10:c11 -> c38:c39:c40:c41 -> c34:c35:c36:c37
zeros :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c35 :: c34:c35:c36:c37
cons :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c36 :: c14:c15 -> c28:c29 -> c42:c43:c44:c45 -> c34:c35:c36:c37
a__and :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
isNatIListKind :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c37 :: c34:c35:c36:c37
nil :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c38 :: c38:c39:c40:c41
c39 :: c38:c39:c40:c41
c40 :: c28:c29 -> c42:c43:c44:c45 -> c38:c39:c40:c41
c41 :: c38:c39:c40:c41
c42 :: c42:c43:c44:c45
c43 :: c38:c39:c40:c41 -> c42:c43:c44:c45
c44 :: c42:c43:c44:c45 -> c42:c43:c44:c45
c45 :: c42:c43:c44:c45
c46 :: c46:c47:c48
c47 :: c20:c21 -> c28:c29 -> c42:c43:c44:c45 -> c46:c47:c48
c48 :: c46:c47:c48
c49 :: c49:c50:c51
c50 :: c26:c27 -> c28:c29 -> c28:c29 -> c46:c47:c48 -> c49:c50:c51
and :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
isNat :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
isNatKind :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c51 :: c49:c50:c51
c52 :: c:c1 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
U11 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c53 :: c2:c3 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
U12 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c54 :: c4:c5 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
isNatList :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c55 :: c46:c47:c48 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
U21 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c56 :: c6:c7 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
U22 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c57 :: c8:c9 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
c58 :: c30:c31:c32:c33 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
U31 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c59 :: c10:c11 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
U32 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c60 :: c12:c13 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
U41 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c61 :: c14:c15 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
U42 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c62 :: c16:c17 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
U43 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c63 :: c18:c19 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
isNatIList :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c64 :: c34:c35:c36:c37 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
U51 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c65 :: c20:c21 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
U52 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c66 :: c22:c23 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
U53 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c67 :: c24:c25 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
U61 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c68 :: c26:c27 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
c69 :: c49:c50:c51 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
c70 :: c28:c29 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
c71 :: c38:c39:c40:c41 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
c72 :: c42:c43:c44:c45 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
c73 :: c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
c74 :: c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
c75 :: c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
c76 :: c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
c77 :: c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
a__zeros :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
a__U11 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
a__U12 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
a__U21 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
a__U22 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
a__U31 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
a__U32 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
a__U41 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
a__U42 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
a__U43 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
a__U51 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
a__U52 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
a__U53 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
a__U61 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
a__length :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
hole_c:c11_78 :: c:c1
hole_c2:c32_78 :: c2:c3
hole_tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U613_78 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
hole_c4:c54_78 :: c4:c5
hole_c46:c47:c485_78 :: c46:c47:c48
hole_c6:c76_78 :: c6:c7
hole_c8:c97_78 :: c8:c9
hole_c30:c31:c32:c338_78 :: c30:c31:c32:c33
hole_c10:c119_78 :: c10:c11
hole_c12:c1310_78 :: c12:c13
hole_c14:c1511_78 :: c14:c15
hole_c16:c1712_78 :: c16:c17
hole_c18:c1913_78 :: c18:c19
hole_c34:c35:c36:c3714_78 :: c34:c35:c36:c37
hole_c20:c2115_78 :: c20:c21
hole_c22:c2316_78 :: c22:c23
hole_c24:c2517_78 :: c24:c25
hole_c26:c2718_78 :: c26:c27
hole_c49:c50:c5119_78 :: c49:c50:c51
hole_c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c7720_78 :: c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
hole_c28:c2921_78 :: c28:c29
hole_c38:c39:c40:c4122_78 :: c38:c39:c40:c41
hole_c42:c43:c44:c4523_78 :: c42:c43:c44:c45
gen_tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U6124_78 :: Nat -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
gen_c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c7725_78 :: Nat -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
gen_c42:c43:c44:c4526_78 :: Nat -> c42:c43:c44:c45

----------------------------------------

(15) OrderProof (LOWER BOUND(ID))
Heuristically decided to analyse the following defined symbols:
A__U11, a__isNatList, A__ISNATLIST, A__U21, a__isNat, A__ISNAT, A__U31, A__U41, A__U42, a__isNatIList, A__ISNATILIST, A__U51, A__U52, A__U61, A__LENGTH, mark, MARK, A__AND, a__isNatIListKind, A__ISNATILISTKIND, a__isNatKind, A__ISNATKIND, a__and, a__U11, a__U21, a__U31, a__U41, a__U42, a__U51, a__U52, a__U61, a__length

They will be analysed ascendingly in the following order:
a__isNatList < A__U11
A__U11 = A__ISNATLIST
A__U11 = A__U21
A__U11 = A__ISNAT
A__U11 = A__U31
A__U11 = A__U41
A__U11 = A__U42
A__U11 = A__ISNATILIST
A__U11 = A__U51
A__U11 = A__U52
A__U11 = A__U61
A__U11 = A__LENGTH
A__U11 = MARK
A__U11 = A__AND
A__U11 = A__ISNATILISTKIND
A__U11 = A__ISNATKIND
a__isNatList = a__isNat
a__isNatList < A__U31
a__isNatList = a__isNatIList
a__isNatList < A__U52
a__isNatList < A__LENGTH
a__isNatList = mark
a__isNatList = a__isNatIListKind
a__isNatList = a__isNatKind
a__isNatList = a__and
a__isNatList = a__U11
a__isNatList = a__U21
a__isNatList = a__U31
a__isNatList = a__U41
a__isNatList = a__U42
a__isNatList = a__U51
a__isNatList = a__U52
a__isNatList = a__U61
a__isNatList = a__length
A__ISNATLIST = A__U21
A__ISNATLIST = A__ISNAT
A__ISNATLIST = A__U31
A__ISNATLIST = A__U41
A__ISNATLIST = A__U42
A__ISNATLIST = A__ISNATILIST
A__ISNATLIST = A__U51
A__ISNATLIST = A__U52
A__ISNATLIST = A__U61
A__ISNATLIST = A__LENGTH
A__ISNATLIST = MARK
A__ISNATLIST = A__AND
A__ISNATLIST = A__ISNATILISTKIND
a__isNatKind < A__ISNATLIST
A__ISNATLIST = A__ISNATKIND
a__and < A__ISNATLIST
a__isNat < A__U21
A__U21 = A__ISNAT
A__U21 = A__U31
A__U21 = A__U41
A__U21 = A__U42
A__U21 = A__ISNATILIST
A__U21 = A__U51
A__U21 = A__U52
A__U21 = A__U61
A__U21 = A__LENGTH
A__U21 = MARK
A__U21 = A__AND
A__U21 = A__ISNATILISTKIND
A__U21 = A__ISNATKIND
a__isNat < A__U41
a__isNat = a__isNatIList
a__isNat < A__U51
a__isNat = mark
a__isNat = a__isNatIListKind
a__isNat = a__isNatKind
a__isNat = a__and
a__isNat = a__U11
a__isNat = a__U21
a__isNat = a__U31
a__isNat = a__U41
a__isNat = a__U42
a__isNat = a__U51
a__isNat = a__U52
a__isNat = a__U61
a__isNat = a__length
A__ISNAT = A__U31
A__ISNAT = A__U41
A__ISNAT = A__U42
A__ISNAT = A__ISNATILIST
A__ISNAT = A__U51
A__ISNAT = A__U52
A__ISNAT = A__U61
A__ISNAT = A__LENGTH
A__ISNAT = MARK
A__ISNAT = A__AND
a__isNatIListKind < A__ISNAT
A__ISNAT = A__ISNATILISTKIND
a__isNatKind < A__ISNAT
A__ISNAT = A__ISNATKIND
A__U31 = A__U41
A__U31 = A__U42
A__U31 = A__ISNATILIST
A__U31 = A__U51
A__U31 = A__U52
A__U31 = A__U61
A__U31 = A__LENGTH
A__U31 = MARK
A__U31 = A__AND
A__U31 = A__ISNATILISTKIND
A__U31 = A__ISNATKIND
A__U41 = A__U42
A__U41 = A__ISNATILIST
A__U41 = A__U51
A__U41 = A__U52
A__U41 = A__U61
A__U41 = A__LENGTH
A__U41 = MARK
A__U41 = A__AND
A__U41 = A__ISNATILISTKIND
A__U41 = A__ISNATKIND
a__isNatIList < A__U42
A__U42 = A__ISNATILIST
A__U42 = A__U51
A__U42 = A__U52
A__U42 = A__U61
A__U42 = A__LENGTH
A__U42 = MARK
A__U42 = A__AND
A__U42 = A__ISNATILISTKIND
A__U42 = A__ISNATKIND
a__isNatIList = mark
a__isNatIList = a__isNatIListKind
a__isNatIList = a__isNatKind
a__isNatIList = a__and
a__isNatIList = a__U11
a__isNatIList = a__U21
a__isNatIList = a__U31
a__isNatIList = a__U41
a__isNatIList = a__U42
a__isNatIList = a__U51
a__isNatIList = a__U52
a__isNatIList = a__U61
a__isNatIList = a__length
A__ISNATILIST = A__U51
A__ISNATILIST = A__U52
A__ISNATILIST = A__U61
A__ISNATILIST = A__LENGTH
A__ISNATILIST = MARK
A__ISNATILIST = A__AND
a__isNatIListKind < A__ISNATILIST
A__ISNATILIST = A__ISNATILISTKIND
a__isNatKind < A__ISNATILIST
A__ISNATILIST = A__ISNATKIND
a__and < A__ISNATILIST
A__U51 = A__U52
A__U51 = A__U61
A__U51 = A__LENGTH
A__U51 = MARK
A__U51 = A__AND
A__U51 = A__ISNATILISTKIND
A__U51 = A__ISNATKIND
A__U52 = A__U61
A__U52 = A__LENGTH
A__U52 = MARK
A__U52 = A__AND
A__U52 = A__ISNATILISTKIND
A__U52 = A__ISNATKIND
A__U61 = A__LENGTH
mark < A__U61
A__U61 = MARK
A__U61 = A__AND
A__U61 = A__ISNATILISTKIND
A__U61 = A__ISNATKIND
A__LENGTH = MARK
A__LENGTH = A__AND
A__LENGTH = A__ISNATILISTKIND
A__LENGTH = A__ISNATKIND
a__and < A__LENGTH
mark < MARK
mark = a__isNatIListKind
mark = a__isNatKind
mark = a__and
mark = a__U11
mark = a__U21
mark = a__U31
mark = a__U41
mark = a__U42
mark = a__U51
mark = a__U52
mark = a__U61
mark = a__length
MARK = A__AND
MARK = A__ISNATILISTKIND
MARK = A__ISNATKIND
A__AND = A__ISNATILISTKIND
A__AND = A__ISNATKIND
a__isNatIListKind = a__isNatKind
a__isNatIListKind = a__and
a__isNatIListKind = a__U11
a__isNatIListKind = a__U21
a__isNatIListKind = a__U31
a__isNatIListKind = a__U41
a__isNatIListKind = a__U42
a__isNatIListKind = a__U51
a__isNatIListKind = a__U52
a__isNatIListKind = a__U61
a__isNatIListKind = a__length
a__isNatKind < A__ISNATILISTKIND
A__ISNATILISTKIND = A__ISNATKIND
a__isNatKind = a__and
a__isNatKind = a__U11
a__isNatKind = a__U21
a__isNatKind = a__U31
a__isNatKind = a__U41
a__isNatKind = a__U42
a__isNatKind = a__U51
a__isNatKind = a__U52
a__isNatKind = a__U61
a__isNatKind = a__length
a__and = a__U11
a__and = a__U21
a__and = a__U31
a__and = a__U41
a__and = a__U42
a__and = a__U51
a__and = a__U52
a__and = a__U61
a__and = a__length
a__U11 = a__U21
a__U11 = a__U31
a__U11 = a__U41
a__U11 = a__U42
a__U11 = a__U51
a__U11 = a__U52
a__U11 = a__U61
a__U11 = a__length
a__U21 = a__U31
a__U21 = a__U41
a__U21 = a__U42
a__U21 = a__U51
a__U21 = a__U52
a__U21 = a__U61
a__U21 = a__length
a__U31 = a__U41
a__U31 = a__U42
a__U31 = a__U51
a__U31 = a__U52
a__U31 = a__U61
a__U31 = a__length
a__U41 = a__U42
a__U41 = a__U51
a__U41 = a__U52
a__U41 = a__U61
a__U41 = a__length
a__U42 = a__U51
a__U42 = a__U52
a__U42 = a__U61
a__U42 = a__length
a__U51 = a__U52
a__U51 = a__U61
a__U51 = a__length
a__U52 = a__U61
a__U52 = a__length
a__U61 = a__length

----------------------------------------

(16)
Obligation:
Innermost TRS:
Rules:
A__ZEROS -> c
A__ZEROS -> c1
A__U11(tt, z0) -> c2(A__U12(a__isNatList(z0)), A__ISNATLIST(z0))
A__U11(z0, z1) -> c3
A__U12(tt) -> c4
A__U12(z0) -> c5
A__U21(tt, z0) -> c6(A__U22(a__isNat(z0)), A__ISNAT(z0))
A__U21(z0, z1) -> c7
A__U22(tt) -> c8
A__U22(z0) -> c9
A__U31(tt, z0) -> c10(A__U32(a__isNatList(z0)), A__ISNATLIST(z0))
A__U31(z0, z1) -> c11
A__U32(tt) -> c12
A__U32(z0) -> c13
A__U41(tt, z0, z1) -> c14(A__U42(a__isNat(z0), z1), A__ISNAT(z0))
A__U41(z0, z1, z2) -> c15
A__U42(tt, z0) -> c16(A__U43(a__isNatIList(z0)), A__ISNATILIST(z0))
A__U42(z0, z1) -> c17
A__U43(tt) -> c18
A__U43(z0) -> c19
A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0))
A__U51(z0, z1, z2) -> c21
A__U52(tt, z0) -> c22(A__U53(a__isNatList(z0)), A__ISNATLIST(z0))
A__U52(z0, z1) -> c23
A__U53(tt) -> c24
A__U53(z0) -> c25
A__U61(tt, z0) -> 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
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

Types:
A__ZEROS :: c:c1
c :: c:c1
c1 :: c:c1
A__U11 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> c2:c3
tt :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c2 :: c4:c5 -> c46:c47:c48 -> c2:c3
A__U12 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> c4:c5
a__isNatList :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
A__ISNATLIST :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> c46:c47:c48
c3 :: c2:c3
c4 :: c4:c5
c5 :: c4:c5
A__U21 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> c6:c7
c6 :: c8:c9 -> c30:c31:c32:c33 -> c6:c7
A__U22 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> c8:c9
a__isNat :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
A__ISNAT :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> c30:c31:c32:c33
c7 :: c6:c7
c8 :: c8:c9
c9 :: c8:c9
A__U31 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> c10:c11
c10 :: c12:c13 -> c46:c47:c48 -> c10:c11
A__U32 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> c12:c13
c11 :: c10:c11
c12 :: c12:c13
c13 :: c12:c13
A__U41 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> c14:c15
c14 :: c16:c17 -> c30:c31:c32:c33 -> c14:c15
A__U42 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> c16:c17
c15 :: c14:c15
c16 :: c18:c19 -> c34:c35:c36:c37 -> c16:c17
A__U43 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> c18:c19
a__isNatIList :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
A__ISNATILIST :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> c34:c35:c36:c37
c17 :: c16:c17
c18 :: c18:c19
c19 :: c18:c19
A__U51 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> c20:c21
c20 :: c22:c23 -> c30:c31:c32:c33 -> c20:c21
A__U52 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> c22:c23
c21 :: c20:c21
c22 :: c24:c25 -> c46:c47:c48 -> c22:c23
A__U53 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> c24:c25
c23 :: c22:c23
c24 :: c24:c25
c25 :: c24:c25
A__U61 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> c26:c27
c26 :: c49:c50:c51 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77 -> c26:c27
A__LENGTH :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> c49:c50:c51
mark :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
MARK :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
c27 :: c26:c27
A__AND :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> c28:c29
c28 :: c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77 -> c28:c29
c29 :: c28:c29
0' :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c30 :: c30:c31:c32:c33
length :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c31 :: c2:c3 -> c38:c39:c40:c41 -> c30:c31:c32:c33
a__isNatIListKind :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
A__ISNATILISTKIND :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> c38:c39:c40:c41
s :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c32 :: c6:c7 -> c42:c43:c44:c45 -> c30:c31:c32:c33
a__isNatKind :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
A__ISNATKIND :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> c42:c43:c44:c45
c33 :: c30:c31:c32:c33
c34 :: c10:c11 -> c38:c39:c40:c41 -> c34:c35:c36:c37
zeros :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c35 :: c34:c35:c36:c37
cons :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c36 :: c14:c15 -> c28:c29 -> c42:c43:c44:c45 -> c34:c35:c36:c37
a__and :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
isNatIListKind :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c37 :: c34:c35:c36:c37
nil :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c38 :: c38:c39:c40:c41
c39 :: c38:c39:c40:c41
c40 :: c28:c29 -> c42:c43:c44:c45 -> c38:c39:c40:c41
c41 :: c38:c39:c40:c41
c42 :: c42:c43:c44:c45
c43 :: c38:c39:c40:c41 -> c42:c43:c44:c45
c44 :: c42:c43:c44:c45 -> c42:c43:c44:c45
c45 :: c42:c43:c44:c45
c46 :: c46:c47:c48
c47 :: c20:c21 -> c28:c29 -> c42:c43:c44:c45 -> c46:c47:c48
c48 :: c46:c47:c48
c49 :: c49:c50:c51
c50 :: c26:c27 -> c28:c29 -> c28:c29 -> c46:c47:c48 -> c49:c50:c51
and :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
isNat :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
isNatKind :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c51 :: c49:c50:c51
c52 :: c:c1 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
U11 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c53 :: c2:c3 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
U12 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c54 :: c4:c5 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
isNatList :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c55 :: c46:c47:c48 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
U21 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c56 :: c6:c7 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
U22 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c57 :: c8:c9 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
c58 :: c30:c31:c32:c33 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
U31 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c59 :: c10:c11 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
U32 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c60 :: c12:c13 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
U41 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c61 :: c14:c15 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
U42 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c62 :: c16:c17 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
U43 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c63 :: c18:c19 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
isNatIList :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c64 :: c34:c35:c36:c37 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
U51 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c65 :: c20:c21 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
U52 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c66 :: c22:c23 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
U53 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c67 :: c24:c25 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
U61 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
c68 :: c26:c27 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
c69 :: c49:c50:c51 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
c70 :: c28:c29 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
c71 :: c38:c39:c40:c41 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
c72 :: c42:c43:c44:c45 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
c73 :: c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
c74 :: c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
c75 :: c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
c76 :: c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77 -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
c77 :: c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
a__zeros :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
a__U11 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
a__U12 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
a__U21 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
a__U22 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
a__U31 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
a__U32 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
a__U41 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
a__U42 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
a__U43 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
a__U51 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
a__U52 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
a__U53 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
a__U61 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
a__length :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
hole_c:c11_78 :: c:c1
hole_c2:c32_78 :: c2:c3
hole_tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U613_78 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
hole_c4:c54_78 :: c4:c5
hole_c46:c47:c485_78 :: c46:c47:c48
hole_c6:c76_78 :: c6:c7
hole_c8:c97_78 :: c8:c9
hole_c30:c31:c32:c338_78 :: c30:c31:c32:c33
hole_c10:c119_78 :: c10:c11
hole_c12:c1310_78 :: c12:c13
hole_c14:c1511_78 :: c14:c15
hole_c16:c1712_78 :: c16:c17
hole_c18:c1913_78 :: c18:c19
hole_c34:c35:c36:c3714_78 :: c34:c35:c36:c37
hole_c20:c2115_78 :: c20:c21
hole_c22:c2316_78 :: c22:c23
hole_c24:c2517_78 :: c24:c25
hole_c26:c2718_78 :: c26:c27
hole_c49:c50:c5119_78 :: c49:c50:c51
hole_c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c7720_78 :: c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
hole_c28:c2921_78 :: c28:c29
hole_c38:c39:c40:c4122_78 :: c38:c39:c40:c41
hole_c42:c43:c44:c4523_78 :: c42:c43:c44:c45
gen_tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U6124_78 :: Nat -> tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61
gen_c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c7725_78 :: Nat -> c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77
gen_c42:c43:c44:c4526_78 :: Nat -> c42:c43:c44:c45


Generator Equations:
gen_tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U6124_78(0) <=> tt
gen_tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U6124_78(+(x, 1)) <=> length(gen_tt:0':length:s:zeros:cons:isNatIListKind:nil:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U6124_78(x))
gen_c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c7725_78(0) <=> c52(c)
gen_c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c7725_78(+(x, 1)) <=> c53(c2(c4, c46), gen_c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c7725_78(x))
gen_c42:c43:c44:c4526_78(0) <=> c42
gen_c42:c43:c44:c4526_78(+(x, 1)) <=> c44(gen_c42:c43:c44:c4526_78(x))


The following defined symbols remain to be analysed:
a__U51, A__U11, a__isNatList, A__ISNATLIST, A__U21, a__isNat, A__ISNAT, A__U31, A__U41, A__U42, a__isNatIList, A__ISNATILIST, A__U51, A__U52, A__U61, A__LENGTH, mark, MARK, A__AND, a__isNatIListKind, A__ISNATILISTKIND, a__isNatKind, A__ISNATKIND, a__and, a__U11, a__U21, a__U31, a__U41, a__U42, a__U52, a__U61, a__length

They will be analysed ascendingly in the following order:
a__isNatList < A__U11
A__U11 = A__ISNATLIST
A__U11 = A__U21
A__U11 = A__ISNAT
A__U11 = A__U31
A__U11 = A__U41
A__U11 = A__U42
A__U11 = A__ISNATILIST
A__U11 = A__U51
A__U11 = A__U52
A__U11 = A__U61
A__U11 = A__LENGTH
A__U11 = MARK
A__U11 = A__AND
A__U11 = A__ISNATILISTKIND
A__U11 = A__ISNATKIND
a__isNatList = a__isNat
a__isNatList < A__U31
a__isNatList = a__isNatIList
a__isNatList < A__U52
a__isNatList < A__LENGTH
a__isNatList = mark
a__isNatList = a__isNatIListKind
a__isNatList = a__isNatKind
a__isNatList = a__and
a__isNatList = a__U11
a__isNatList = a__U21
a__isNatList = a__U31
a__isNatList = a__U41
a__isNatList = a__U42
a__isNatList = a__U51
a__isNatList = a__U52
a__isNatList = a__U61
a__isNatList = a__length
A__ISNATLIST = A__U21
A__ISNATLIST = A__ISNAT
A__ISNATLIST = A__U31
A__ISNATLIST = A__U41
A__ISNATLIST = A__U42
A__ISNATLIST = A__ISNATILIST
A__ISNATLIST = A__U51
A__ISNATLIST = A__U52
A__ISNATLIST = A__U61
A__ISNATLIST = A__LENGTH
A__ISNATLIST = MARK
A__ISNATLIST = A__AND
A__ISNATLIST = A__ISNATILISTKIND
a__isNatKind < A__ISNATLIST
A__ISNATLIST = A__ISNATKIND
a__and < A__ISNATLIST
a__isNat < A__U21
A__U21 = A__ISNAT
A__U21 = A__U31
A__U21 = A__U41
A__U21 = A__U42
A__U21 = A__ISNATILIST
A__U21 = A__U51
A__U21 = A__U52
A__U21 = A__U61
A__U21 = A__LENGTH
A__U21 = MARK
A__U21 = A__AND
A__U21 = A__ISNATILISTKIND
A__U21 = A__ISNATKIND
a__isNat < A__U41
a__isNat = a__isNatIList
a__isNat < A__U51
a__isNat = mark
a__isNat = a__isNatIListKind
a__isNat = a__isNatKind
a__isNat = a__and
a__isNat = a__U11
a__isNat = a__U21
a__isNat = a__U31
a__isNat = a__U41
a__isNat = a__U42
a__isNat = a__U51
a__isNat = a__U52
a__isNat = a__U61
a__isNat = a__length
A__ISNAT = A__U31
A__ISNAT = A__U41
A__ISNAT = A__U42
A__ISNAT = A__ISNATILIST
A__ISNAT = A__U51
A__ISNAT = A__U52
A__ISNAT = A__U61
A__ISNAT = A__LENGTH
A__ISNAT = MARK
A__ISNAT = A__AND
a__isNatIListKind < A__ISNAT
A__ISNAT = A__ISNATILISTKIND
a__isNatKind < A__ISNAT
A__ISNAT = A__ISNATKIND
A__U31 = A__U41
A__U31 = A__U42
A__U31 = A__ISNATILIST
A__U31 = A__U51
A__U31 = A__U52
A__U31 = A__U61
A__U31 = A__LENGTH
A__U31 = MARK
A__U31 = A__AND
A__U31 = A__ISNATILISTKIND
A__U31 = A__ISNATKIND
A__U41 = A__U42
A__U41 = A__ISNATILIST
A__U41 = A__U51
A__U41 = A__U52
A__U41 = A__U61
A__U41 = A__LENGTH
A__U41 = MARK
A__U41 = A__AND
A__U41 = A__ISNATILISTKIND
A__U41 = A__ISNATKIND
a__isNatIList < A__U42
A__U42 = A__ISNATILIST
A__U42 = A__U51
A__U42 = A__U52
A__U42 = A__U61
A__U42 = A__LENGTH
A__U42 = MARK
A__U42 = A__AND
A__U42 = A__ISNATILISTKIND
A__U42 = A__ISNATKIND
a__isNatIList = mark
a__isNatIList = a__isNatIListKind
a__isNatIList = a__isNatKind
a__isNatIList = a__and
a__isNatIList = a__U11
a__isNatIList = a__U21
a__isNatIList = a__U31
a__isNatIList = a__U41
a__isNatIList = a__U42
a__isNatIList = a__U51
a__isNatIList = a__U52
a__isNatIList = a__U61
a__isNatIList = a__length
A__ISNATILIST = A__U51
A__ISNATILIST = A__U52
A__ISNATILIST = A__U61
A__ISNATILIST = A__LENGTH
A__ISNATILIST = MARK
A__ISNATILIST = A__AND
a__isNatIListKind < A__ISNATILIST
A__ISNATILIST = A__ISNATILISTKIND
a__isNatKind < A__ISNATILIST
A__ISNATILIST = A__ISNATKIND
a__and < A__ISNATILIST
A__U51 = A__U52
A__U51 = A__U61
A__U51 = A__LENGTH
A__U51 = MARK
A__U51 = A__AND
A__U51 = A__ISNATILISTKIND
A__U51 = A__ISNATKIND
A__U52 = A__U61
A__U52 = A__LENGTH
A__U52 = MARK
A__U52 = A__AND
A__U52 = A__ISNATILISTKIND
A__U52 = A__ISNATKIND
A__U61 = A__LENGTH
mark < A__U61
A__U61 = MARK
A__U61 = A__AND
A__U61 = A__ISNATILISTKIND
A__U61 = A__ISNATKIND
A__LENGTH = MARK
A__LENGTH = A__AND
A__LENGTH = A__ISNATILISTKIND
A__LENGTH = A__ISNATKIND
a__and < A__LENGTH
mark < MARK
mark = a__isNatIListKind
mark = a__isNatKind
mark = a__and
mark = a__U11
mark = a__U21
mark = a__U31
mark = a__U41
mark = a__U42
mark = a__U51
mark = a__U52
mark = a__U61
mark = a__length
MARK = A__AND
MARK = A__ISNATILISTKIND
MARK = A__ISNATKIND
A__AND = A__ISNATILISTKIND
A__AND = A__ISNATKIND
a__isNatIListKind = a__isNatKind
a__isNatIListKind = a__and
a__isNatIListKind = a__U11
a__isNatIListKind = a__U21
a__isNatIListKind = a__U31
a__isNatIListKind = a__U41
a__isNatIListKind = a__U42
a__isNatIListKind = a__U51
a__isNatIListKind = a__U52
a__isNatIListKind = a__U61
a__isNatIListKind = a__length
a__isNatKind < A__ISNATILISTKIND
A__ISNATILISTKIND = A__ISNATKIND
a__isNatKind = a__and
a__isNatKind = a__U11
a__isNatKind = a__U21
a__isNatKind = a__U31
a__isNatKind = a__U41
a__isNatKind = a__U42
a__isNatKind = a__U51
a__isNatKind = a__U52
a__isNatKind = a__U61
a__isNatKind = a__length
a__and = a__U11
a__and = a__U21
a__and = a__U31
a__and = a__U41
a__and = a__U42
a__and = a__U51
a__and = a__U52
a__and = a__U61
a__and = a__length
a__U11 = a__U21
a__U11 = a__U31
a__U11 = a__U41
a__U11 = a__U42
a__U11 = a__U51
a__U11 = a__U52
a__U11 = a__U61
a__U11 = a__length
a__U21 = a__U31
a__U21 = a__U41
a__U21 = a__U42
a__U21 = a__U51
a__U21 = a__U52
a__U21 = a__U61
a__U21 = a__length
a__U31 = a__U41
a__U31 = a__U42
a__U31 = a__U51
a__U31 = a__U52
a__U31 = a__U61
a__U31 = a__length
a__U41 = a__U42
a__U41 = a__U51
a__U41 = a__U52
a__U41 = a__U61
a__U41 = a__length
a__U42 = a__U51
a__U42 = a__U52
a__U42 = a__U61
a__U42 = a__length
a__U51 = a__U52
a__U51 = a__U61
a__U51 = a__length
a__U52 = a__U61
a__U52 = a__length
a__U61 = a__length

----------------------------------------

(17) CpxTrsToCdtProof (UPPER BOUND(ID))
Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT
----------------------------------------

(18)
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


----------------------------------------

(19) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 38 trailing nodes:
   MARK(nil) -> c77
   A__U32(z0) -> c13
   A__ISNAT(z0) -> c33
   A__U21(z0, z1) -> c7
   A__U12(tt) -> c4
   A__LENGTH(z0) -> c51
   A__ISNATILISTKIND(z0) -> c41
   A__ISNATKIND(0) -> c42
   A__ZEROS -> c1
   MARK(zeros) -> c52(A__ZEROS)
   A__AND(z0, z1) -> c29
   A__U53(z0) -> c25
   MARK(tt) -> c75
   A__ISNAT(0) -> c30
   A__U42(z0, z1) -> c17
   A__U32(tt) -> c12
   A__U12(z0) -> c5
   A__U61(z0, z1) -> c27
   A__LENGTH(nil) -> c49
   A__U53(tt) -> c24
   A__ISNATILISTKIND(nil) -> c38
   A__U51(z0, z1, z2) -> c21
   A__U22(z0) -> c9
   A__U22(tt) -> c8
   A__U31(z0, z1) -> c11
   A__ISNATILIST(zeros) -> c35
   A__U11(z0, z1) -> c3
   A__ISNATILISTKIND(zeros) -> c39
   A__U43(z0) -> c19
   MARK(0) -> c74
   A__ISNATLIST(z0) -> c48
   A__ISNATLIST(nil) -> c46
   A__ISNATKIND(z0) -> c45
   A__U52(z0, z1) -> c23
   A__U41(z0, z1, z2) -> c15
   A__U43(tt) -> c18
   A__ZEROS -> c
   A__ISNATILIST(z0) -> c37

----------------------------------------

(20)
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


----------------------------------------

(21) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 10 trailing tuple parts
----------------------------------------

(22)
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


----------------------------------------

(23) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID))
Converted S to standard rules, and D \ S as well as R to relative rules.
----------------------------------------

(24)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   A__U41(tt, z0, z1) -> c14(A__U42(a__isNat(z0), z1), A__ISNAT(z0))
   A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0))
   A__U61(tt, z0) -> 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))

The (relative) TRS S consists of the following rules:

   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0) -> 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

Rewrite Strategy: INNERMOST
----------------------------------------

(25) RelTrsToTrsProof (UPPER BOUND(ID))
transformed relative TRS to TRS
----------------------------------------

(26)
Obligation:
The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   A__U41(tt, z0, z1) -> c14(A__U42(a__isNat(z0), z1), A__ISNAT(z0))
   A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0))
   A__U61(tt, z0) -> 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__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

S is empty.
Rewrite Strategy: INNERMOST
----------------------------------------

(27) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
Transformed relative TRS to weighted TRS
----------------------------------------

(28)
Obligation:
The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   A__U41(tt, z0, z1) -> c14(A__U42(a__isNat(z0), z1), A__ISNAT(z0)) [1]
   A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0)) [1]
   A__U61(tt, z0) -> c26(A__LENGTH(mark(z0)), MARK(z0)) [1]
   A__AND(tt, z0) -> c28(MARK(z0)) [1]
   A__ISNAT(length(z0)) -> c31(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) [1]
   A__ISNAT(s(z0)) -> c32(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) [1]
   A__ISNATILIST(z0) -> c34(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) [1]
   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)) [1]
   A__ISNATILISTKIND(cons(z0, z1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) [1]
   A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) [1]
   A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) [1]
   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)) [1]
   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)) [1]
   MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) [1]
   MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) [1]
   MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) [1]
   MARK(isNat(z0)) -> c58(A__ISNAT(z0)) [1]
   MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) [1]
   MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) [1]
   MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) [1]
   MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) [1]
   MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) [1]
   MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) [1]
   MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) [1]
   MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) [1]
   MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) [1]
   MARK(cons(z0, z1)) -> c73(MARK(z0)) [1]
   MARK(s(z0)) -> c76(MARK(z0)) [1]
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) [1]
   A__U21(tt, z0) -> c6(A__ISNAT(z0)) [1]
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) [1]
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) [1]
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) [1]
   MARK(U12(z0)) -> c54(MARK(z0)) [1]
   MARK(U22(z0)) -> c57(MARK(z0)) [1]
   MARK(U32(z0)) -> c60(MARK(z0)) [1]
   MARK(U43(z0)) -> c63(MARK(z0)) [1]
   MARK(U53(z0)) -> c67(MARK(z0)) [1]
   a__zeros -> cons(0, zeros) [0]
   a__zeros -> zeros [0]
   a__U11(tt, z0) -> a__U12(a__isNatList(z0)) [0]
   a__U11(z0, z1) -> U11(z0, z1) [0]
   a__U12(tt) -> tt [0]
   a__U12(z0) -> U12(z0) [0]
   a__U21(tt, z0) -> a__U22(a__isNat(z0)) [0]
   a__U21(z0, z1) -> U21(z0, z1) [0]
   a__U22(tt) -> tt [0]
   a__U22(z0) -> U22(z0) [0]
   a__U31(tt, z0) -> a__U32(a__isNatList(z0)) [0]
   a__U31(z0, z1) -> U31(z0, z1) [0]
   a__U32(tt) -> tt [0]
   a__U32(z0) -> U32(z0) [0]
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) [0]
   a__U41(z0, z1, z2) -> U41(z0, z1, z2) [0]
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) [0]
   a__U42(z0, z1) -> U42(z0, z1) [0]
   a__U43(tt) -> tt [0]
   a__U43(z0) -> U43(z0) [0]
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) [0]
   a__U51(z0, z1, z2) -> U51(z0, z1, z2) [0]
   a__U52(tt, z0) -> a__U53(a__isNatList(z0)) [0]
   a__U52(z0, z1) -> U52(z0, z1) [0]
   a__U53(tt) -> tt [0]
   a__U53(z0) -> U53(z0) [0]
   a__U61(tt, z0) -> s(a__length(mark(z0))) [0]
   a__U61(z0, z1) -> U61(z0, z1) [0]
   a__and(tt, z0) -> mark(z0) [0]
   a__and(z0, z1) -> and(z0, z1) [0]
   a__isNat(0) -> tt [0]
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) [0]
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) [0]
   a__isNat(z0) -> isNat(z0) [0]
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) [0]
   a__isNatIList(zeros) -> tt [0]
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) [0]
   a__isNatIList(z0) -> isNatIList(z0) [0]
   a__isNatIListKind(nil) -> tt [0]
   a__isNatIListKind(zeros) -> tt [0]
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) [0]
   a__isNatIListKind(z0) -> isNatIListKind(z0) [0]
   a__isNatKind(0) -> tt [0]
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0) [0]
   a__isNatKind(s(z0)) -> a__isNatKind(z0) [0]
   a__isNatKind(z0) -> isNatKind(z0) [0]
   a__isNatList(nil) -> tt [0]
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) [0]
   a__isNatList(z0) -> isNatList(z0) [0]
   a__length(nil) -> 0 [0]
   a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) [0]
   a__length(z0) -> length(z0) [0]
   mark(zeros) -> a__zeros [0]
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1) [0]
   mark(U12(z0)) -> a__U12(mark(z0)) [0]
   mark(isNatList(z0)) -> a__isNatList(z0) [0]
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1) [0]
   mark(U22(z0)) -> a__U22(mark(z0)) [0]
   mark(isNat(z0)) -> a__isNat(z0) [0]
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1) [0]
   mark(U32(z0)) -> a__U32(mark(z0)) [0]
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) [0]
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1) [0]
   mark(U43(z0)) -> a__U43(mark(z0)) [0]
   mark(isNatIList(z0)) -> a__isNatIList(z0) [0]
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) [0]
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1) [0]
   mark(U53(z0)) -> a__U53(mark(z0)) [0]
   mark(U61(z0, z1)) -> a__U61(mark(z0), z1) [0]
   mark(length(z0)) -> a__length(mark(z0)) [0]
   mark(and(z0, z1)) -> a__and(mark(z0), z1) [0]
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) [0]
   mark(isNatKind(z0)) -> a__isNatKind(z0) [0]
   mark(cons(z0, z1)) -> cons(mark(z0), z1) [0]
   mark(0) -> 0 [0]
   mark(tt) -> tt [0]
   mark(s(z0)) -> s(mark(z0)) [0]
   mark(nil) -> nil [0]

Rewrite Strategy: INNERMOST
----------------------------------------

(29) TypeInferenceProof (BOTH BOUNDS(ID, ID))
Infered types.
----------------------------------------

(30)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   A__U41(tt, z0, z1) -> c14(A__U42(a__isNat(z0), z1), A__ISNAT(z0)) [1]
   A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0)) [1]
   A__U61(tt, z0) -> c26(A__LENGTH(mark(z0)), MARK(z0)) [1]
   A__AND(tt, z0) -> c28(MARK(z0)) [1]
   A__ISNAT(length(z0)) -> c31(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) [1]
   A__ISNAT(s(z0)) -> c32(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) [1]
   A__ISNATILIST(z0) -> c34(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) [1]
   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)) [1]
   A__ISNATILISTKIND(cons(z0, z1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) [1]
   A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) [1]
   A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) [1]
   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)) [1]
   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)) [1]
   MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) [1]
   MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) [1]
   MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) [1]
   MARK(isNat(z0)) -> c58(A__ISNAT(z0)) [1]
   MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) [1]
   MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) [1]
   MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) [1]
   MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) [1]
   MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) [1]
   MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) [1]
   MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) [1]
   MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) [1]
   MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) [1]
   MARK(cons(z0, z1)) -> c73(MARK(z0)) [1]
   MARK(s(z0)) -> c76(MARK(z0)) [1]
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) [1]
   A__U21(tt, z0) -> c6(A__ISNAT(z0)) [1]
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) [1]
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) [1]
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) [1]
   MARK(U12(z0)) -> c54(MARK(z0)) [1]
   MARK(U22(z0)) -> c57(MARK(z0)) [1]
   MARK(U32(z0)) -> c60(MARK(z0)) [1]
   MARK(U43(z0)) -> c63(MARK(z0)) [1]
   MARK(U53(z0)) -> c67(MARK(z0)) [1]
   a__zeros -> cons(0, zeros) [0]
   a__zeros -> zeros [0]
   a__U11(tt, z0) -> a__U12(a__isNatList(z0)) [0]
   a__U11(z0, z1) -> U11(z0, z1) [0]
   a__U12(tt) -> tt [0]
   a__U12(z0) -> U12(z0) [0]
   a__U21(tt, z0) -> a__U22(a__isNat(z0)) [0]
   a__U21(z0, z1) -> U21(z0, z1) [0]
   a__U22(tt) -> tt [0]
   a__U22(z0) -> U22(z0) [0]
   a__U31(tt, z0) -> a__U32(a__isNatList(z0)) [0]
   a__U31(z0, z1) -> U31(z0, z1) [0]
   a__U32(tt) -> tt [0]
   a__U32(z0) -> U32(z0) [0]
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) [0]
   a__U41(z0, z1, z2) -> U41(z0, z1, z2) [0]
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) [0]
   a__U42(z0, z1) -> U42(z0, z1) [0]
   a__U43(tt) -> tt [0]
   a__U43(z0) -> U43(z0) [0]
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) [0]
   a__U51(z0, z1, z2) -> U51(z0, z1, z2) [0]
   a__U52(tt, z0) -> a__U53(a__isNatList(z0)) [0]
   a__U52(z0, z1) -> U52(z0, z1) [0]
   a__U53(tt) -> tt [0]
   a__U53(z0) -> U53(z0) [0]
   a__U61(tt, z0) -> s(a__length(mark(z0))) [0]
   a__U61(z0, z1) -> U61(z0, z1) [0]
   a__and(tt, z0) -> mark(z0) [0]
   a__and(z0, z1) -> and(z0, z1) [0]
   a__isNat(0) -> tt [0]
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) [0]
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) [0]
   a__isNat(z0) -> isNat(z0) [0]
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) [0]
   a__isNatIList(zeros) -> tt [0]
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) [0]
   a__isNatIList(z0) -> isNatIList(z0) [0]
   a__isNatIListKind(nil) -> tt [0]
   a__isNatIListKind(zeros) -> tt [0]
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) [0]
   a__isNatIListKind(z0) -> isNatIListKind(z0) [0]
   a__isNatKind(0) -> tt [0]
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0) [0]
   a__isNatKind(s(z0)) -> a__isNatKind(z0) [0]
   a__isNatKind(z0) -> isNatKind(z0) [0]
   a__isNatList(nil) -> tt [0]
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) [0]
   a__isNatList(z0) -> isNatList(z0) [0]
   a__length(nil) -> 0 [0]
   a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) [0]
   a__length(z0) -> length(z0) [0]
   mark(zeros) -> a__zeros [0]
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1) [0]
   mark(U12(z0)) -> a__U12(mark(z0)) [0]
   mark(isNatList(z0)) -> a__isNatList(z0) [0]
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1) [0]
   mark(U22(z0)) -> a__U22(mark(z0)) [0]
   mark(isNat(z0)) -> a__isNat(z0) [0]
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1) [0]
   mark(U32(z0)) -> a__U32(mark(z0)) [0]
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) [0]
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1) [0]
   mark(U43(z0)) -> a__U43(mark(z0)) [0]
   mark(isNatIList(z0)) -> a__isNatIList(z0) [0]
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) [0]
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1) [0]
   mark(U53(z0)) -> a__U53(mark(z0)) [0]
   mark(U61(z0, z1)) -> a__U61(mark(z0), z1) [0]
   mark(length(z0)) -> a__length(mark(z0)) [0]
   mark(and(z0, z1)) -> a__and(mark(z0), z1) [0]
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) [0]
   mark(isNatKind(z0)) -> a__isNatKind(z0) [0]
   mark(cons(z0, z1)) -> cons(mark(z0), z1) [0]
   mark(0) -> 0 [0]
   mark(tt) -> tt [0]
   mark(s(z0)) -> s(mark(z0)) [0]
   mark(nil) -> nil [0]

The TRS has the following type information:
A__U41 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> c14
tt :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
c14 :: c16 -> c31:c32 -> c14
A__U42 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> c16
a__isNat :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
A__ISNAT :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> c31:c32
A__U51 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> c20
c20 :: c22 -> c31:c32 -> c20
A__U52 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> c22
A__U61 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> c26
c26 :: c50 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c26
A__LENGTH :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> c50
mark :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
MARK :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
A__AND :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> c28
c28 :: c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c28
length :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
c31 :: c2 -> c40 -> c31:c32
A__U11 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> c2
a__isNatIListKind :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
A__ISNATILISTKIND :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> c40
s :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
c32 :: c6 -> c43:c44 -> c31:c32
A__U21 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> c6
a__isNatKind :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
A__ISNATKIND :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> c43:c44
A__ISNATILIST :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> c34:c36
c34 :: c10 -> c40 -> c34:c36
A__U31 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> c10
cons :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
c36 :: c14 -> c28 -> c43:c44 -> c34:c36
a__and :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
isNatIListKind :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
c40 :: c28 -> c43:c44 -> c40
c43 :: c40 -> c43:c44
c44 :: c43:c44 -> c43:c44
A__ISNATLIST :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> c47
c47 :: c20 -> c28 -> c43:c44 -> c47
c50 :: c26 -> c28 -> c28 -> c47 -> c50
a__isNatList :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
and :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
isNat :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
isNatKind :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
U11 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
c53 :: c2 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
isNatList :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
c55 :: c47 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
U21 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
c56 :: c6 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
c58 :: c31:c32 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
U31 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
c59 :: c10 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
U41 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
c61 :: c14 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
U42 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
c62 :: c16 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
isNatIList :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
c64 :: c34:c36 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
U51 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
c65 :: c20 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
U52 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
c66 :: c22 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
U61 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
c68 :: c26 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
c69 :: c50 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
c70 :: c28 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
c71 :: c40 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
c72 :: c43:c44 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
c73 :: c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
c76 :: c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
c2 :: c47 -> c2
c6 :: c31:c32 -> c6
c10 :: c47 -> c10
c16 :: c34:c36 -> c16
c22 :: c47 -> c22
U12 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
c54 :: c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
U22 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
c57 :: c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
U32 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
c60 :: c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
U43 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
c63 :: c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
U53 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
c67 :: c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
a__zeros :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
0 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
zeros :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
a__U11 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
a__U12 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
a__U21 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
a__U22 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
a__U31 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
a__U32 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
a__U41 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
a__U42 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
a__U43 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
a__isNatIList :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
a__U51 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
a__U52 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
a__U53 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
a__U61 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
a__length :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil
nil :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil

Rewrite Strategy: INNERMOST
----------------------------------------

(31) CompletionProof (UPPER BOUND(ID))
The transformation into a RNTS is sound, since:

(a) The obligation is a constructor system where every type has a constant constructor,

(b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols:

   A__U41_3
   A__U51_3
   A__U61_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

(c) The following functions are completely defined:

   a__zeros
   a__U11_2
   a__U12_1
   a__U21_2
   a__U22_1
   a__U31_2
   a__U32_1
   a__U41_3
   a__U42_2
   a__U43_1
   a__U51_3
   a__U52_2
   a__U53_1
   a__U61_2
   a__and_2
   a__isNat_1
   a__isNatIList_1
   a__isNatIListKind_1
   a__isNatKind_1
   a__isNatList_1
   a__length_1
   mark_1

Due to the following rules being added:

   a__zeros -> null_a__zeros [0]
   a__U11(v0, v1) -> null_a__U11 [0]
   a__U12(v0) -> null_a__U12 [0]
   a__U21(v0, v1) -> null_a__U21 [0]
   a__U22(v0) -> null_a__U22 [0]
   a__U31(v0, v1) -> null_a__U31 [0]
   a__U32(v0) -> null_a__U32 [0]
   a__U41(v0, v1, v2) -> null_a__U41 [0]
   a__U42(v0, v1) -> null_a__U42 [0]
   a__U43(v0) -> null_a__U43 [0]
   a__U51(v0, v1, v2) -> null_a__U51 [0]
   a__U52(v0, v1) -> null_a__U52 [0]
   a__U53(v0) -> null_a__U53 [0]
   a__U61(v0, v1) -> null_a__U61 [0]
   a__and(v0, v1) -> null_a__and [0]
   a__isNat(v0) -> null_a__isNat [0]
   a__isNatIList(v0) -> null_a__isNatIList [0]
   a__isNatIListKind(v0) -> null_a__isNatIListKind [0]
   a__isNatKind(v0) -> null_a__isNatKind [0]
   a__isNatList(v0) -> null_a__isNatList [0]
   a__length(v0) -> null_a__length [0]
   mark(v0) -> null_mark [0]

And the following fresh constants:    null_a__zeros, null_a__U11, null_a__U12, null_a__U21, null_a__U22, null_a__U31, null_a__U32, null_a__U41, null_a__U42, null_a__U43, null_a__U51, null_a__U52, null_a__U53, null_a__U61, null_a__and, null_a__isNat, null_a__isNatIList, null_a__isNatIListKind, null_a__isNatKind, null_a__isNatList, null_a__length, null_mark, const, const1, const2, const3, const4, const5, const6, const7, const8, const9, const10, const11, const12, const13, const14, const15

----------------------------------------

(32)
Obligation:
Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:

Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   A__U41(tt, z0, z1) -> c14(A__U42(a__isNat(z0), z1), A__ISNAT(z0)) [1]
   A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0)) [1]
   A__U61(tt, z0) -> c26(A__LENGTH(mark(z0)), MARK(z0)) [1]
   A__AND(tt, z0) -> c28(MARK(z0)) [1]
   A__ISNAT(length(z0)) -> c31(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) [1]
   A__ISNAT(s(z0)) -> c32(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) [1]
   A__ISNATILIST(z0) -> c34(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) [1]
   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)) [1]
   A__ISNATILISTKIND(cons(z0, z1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) [1]
   A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) [1]
   A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) [1]
   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)) [1]
   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)) [1]
   MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) [1]
   MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) [1]
   MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) [1]
   MARK(isNat(z0)) -> c58(A__ISNAT(z0)) [1]
   MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) [1]
   MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) [1]
   MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) [1]
   MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) [1]
   MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) [1]
   MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) [1]
   MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) [1]
   MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) [1]
   MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) [1]
   MARK(cons(z0, z1)) -> c73(MARK(z0)) [1]
   MARK(s(z0)) -> c76(MARK(z0)) [1]
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) [1]
   A__U21(tt, z0) -> c6(A__ISNAT(z0)) [1]
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) [1]
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) [1]
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) [1]
   MARK(U12(z0)) -> c54(MARK(z0)) [1]
   MARK(U22(z0)) -> c57(MARK(z0)) [1]
   MARK(U32(z0)) -> c60(MARK(z0)) [1]
   MARK(U43(z0)) -> c63(MARK(z0)) [1]
   MARK(U53(z0)) -> c67(MARK(z0)) [1]
   a__zeros -> cons(0, zeros) [0]
   a__zeros -> zeros [0]
   a__U11(tt, z0) -> a__U12(a__isNatList(z0)) [0]
   a__U11(z0, z1) -> U11(z0, z1) [0]
   a__U12(tt) -> tt [0]
   a__U12(z0) -> U12(z0) [0]
   a__U21(tt, z0) -> a__U22(a__isNat(z0)) [0]
   a__U21(z0, z1) -> U21(z0, z1) [0]
   a__U22(tt) -> tt [0]
   a__U22(z0) -> U22(z0) [0]
   a__U31(tt, z0) -> a__U32(a__isNatList(z0)) [0]
   a__U31(z0, z1) -> U31(z0, z1) [0]
   a__U32(tt) -> tt [0]
   a__U32(z0) -> U32(z0) [0]
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) [0]
   a__U41(z0, z1, z2) -> U41(z0, z1, z2) [0]
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) [0]
   a__U42(z0, z1) -> U42(z0, z1) [0]
   a__U43(tt) -> tt [0]
   a__U43(z0) -> U43(z0) [0]
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) [0]
   a__U51(z0, z1, z2) -> U51(z0, z1, z2) [0]
   a__U52(tt, z0) -> a__U53(a__isNatList(z0)) [0]
   a__U52(z0, z1) -> U52(z0, z1) [0]
   a__U53(tt) -> tt [0]
   a__U53(z0) -> U53(z0) [0]
   a__U61(tt, z0) -> s(a__length(mark(z0))) [0]
   a__U61(z0, z1) -> U61(z0, z1) [0]
   a__and(tt, z0) -> mark(z0) [0]
   a__and(z0, z1) -> and(z0, z1) [0]
   a__isNat(0) -> tt [0]
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) [0]
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) [0]
   a__isNat(z0) -> isNat(z0) [0]
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) [0]
   a__isNatIList(zeros) -> tt [0]
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) [0]
   a__isNatIList(z0) -> isNatIList(z0) [0]
   a__isNatIListKind(nil) -> tt [0]
   a__isNatIListKind(zeros) -> tt [0]
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) [0]
   a__isNatIListKind(z0) -> isNatIListKind(z0) [0]
   a__isNatKind(0) -> tt [0]
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0) [0]
   a__isNatKind(s(z0)) -> a__isNatKind(z0) [0]
   a__isNatKind(z0) -> isNatKind(z0) [0]
   a__isNatList(nil) -> tt [0]
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) [0]
   a__isNatList(z0) -> isNatList(z0) [0]
   a__length(nil) -> 0 [0]
   a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) [0]
   a__length(z0) -> length(z0) [0]
   mark(zeros) -> a__zeros [0]
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1) [0]
   mark(U12(z0)) -> a__U12(mark(z0)) [0]
   mark(isNatList(z0)) -> a__isNatList(z0) [0]
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1) [0]
   mark(U22(z0)) -> a__U22(mark(z0)) [0]
   mark(isNat(z0)) -> a__isNat(z0) [0]
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1) [0]
   mark(U32(z0)) -> a__U32(mark(z0)) [0]
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) [0]
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1) [0]
   mark(U43(z0)) -> a__U43(mark(z0)) [0]
   mark(isNatIList(z0)) -> a__isNatIList(z0) [0]
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) [0]
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1) [0]
   mark(U53(z0)) -> a__U53(mark(z0)) [0]
   mark(U61(z0, z1)) -> a__U61(mark(z0), z1) [0]
   mark(length(z0)) -> a__length(mark(z0)) [0]
   mark(and(z0, z1)) -> a__and(mark(z0), z1) [0]
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) [0]
   mark(isNatKind(z0)) -> a__isNatKind(z0) [0]
   mark(cons(z0, z1)) -> cons(mark(z0), z1) [0]
   mark(0) -> 0 [0]
   mark(tt) -> tt [0]
   mark(s(z0)) -> s(mark(z0)) [0]
   mark(nil) -> nil [0]
   a__zeros -> null_a__zeros [0]
   a__U11(v0, v1) -> null_a__U11 [0]
   a__U12(v0) -> null_a__U12 [0]
   a__U21(v0, v1) -> null_a__U21 [0]
   a__U22(v0) -> null_a__U22 [0]
   a__U31(v0, v1) -> null_a__U31 [0]
   a__U32(v0) -> null_a__U32 [0]
   a__U41(v0, v1, v2) -> null_a__U41 [0]
   a__U42(v0, v1) -> null_a__U42 [0]
   a__U43(v0) -> null_a__U43 [0]
   a__U51(v0, v1, v2) -> null_a__U51 [0]
   a__U52(v0, v1) -> null_a__U52 [0]
   a__U53(v0) -> null_a__U53 [0]
   a__U61(v0, v1) -> null_a__U61 [0]
   a__and(v0, v1) -> null_a__and [0]
   a__isNat(v0) -> null_a__isNat [0]
   a__isNatIList(v0) -> null_a__isNatIList [0]
   a__isNatIListKind(v0) -> null_a__isNatIListKind [0]
   a__isNatKind(v0) -> null_a__isNatKind [0]
   a__isNatList(v0) -> null_a__isNatList [0]
   a__length(v0) -> null_a__length [0]
   mark(v0) -> null_mark [0]

The TRS has the following type information:
A__U41 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c14
tt :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c14 :: c16 -> c31:c32 -> c14
A__U42 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c16
a__isNat :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
A__ISNAT :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c31:c32
A__U51 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c20
c20 :: c22 -> c31:c32 -> c20
A__U52 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c22
A__U61 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c26
c26 :: c50 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c26
A__LENGTH :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c50
mark :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
MARK :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
A__AND :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c28
c28 :: c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c28
length :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c31 :: c2 -> c40 -> c31:c32
A__U11 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c2
a__isNatIListKind :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
A__ISNATILISTKIND :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c40
s :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c32 :: c6 -> c43:c44 -> c31:c32
A__U21 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c6
a__isNatKind :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
A__ISNATKIND :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c43:c44
A__ISNATILIST :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c34:c36
c34 :: c10 -> c40 -> c34:c36
A__U31 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c10
cons :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c36 :: c14 -> c28 -> c43:c44 -> c34:c36
a__and :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
isNatIListKind :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c40 :: c28 -> c43:c44 -> c40
c43 :: c40 -> c43:c44
c44 :: c43:c44 -> c43:c44
A__ISNATLIST :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c47
c47 :: c20 -> c28 -> c43:c44 -> c47
c50 :: c26 -> c28 -> c28 -> c47 -> c50
a__isNatList :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
and :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
isNat :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
isNatKind :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
U11 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c53 :: c2 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
isNatList :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c55 :: c47 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
U21 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c56 :: c6 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
c58 :: c31:c32 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
U31 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c59 :: c10 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
U41 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c61 :: c14 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
U42 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c62 :: c16 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
isNatIList :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c64 :: c34:c36 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
U51 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c65 :: c20 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
U52 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c66 :: c22 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
U61 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c68 :: c26 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
c69 :: c50 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
c70 :: c28 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
c71 :: c40 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
c72 :: c43:c44 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
c73 :: c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
c76 :: c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
c2 :: c47 -> c2
c6 :: c31:c32 -> c6
c10 :: c47 -> c10
c16 :: c34:c36 -> c16
c22 :: c47 -> c22
U12 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c54 :: c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
U22 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c57 :: c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
U32 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c60 :: c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
U43 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c63 :: c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
U53 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c67 :: c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
a__zeros :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
0 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
zeros :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__U11 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__U12 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__U21 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__U22 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__U31 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__U32 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__U41 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__U42 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__U43 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__isNatIList :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__U51 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__U52 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__U53 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__U61 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__length :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
nil :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__zeros :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__U11 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__U12 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__U21 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__U22 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__U31 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__U32 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__U41 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__U42 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__U43 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__U51 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__U52 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__U53 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__U61 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__and :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__isNat :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__isNatIList :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__isNatIListKind :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__isNatKind :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__isNatList :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__length :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_mark :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
const :: c14
const1 :: c16
const2 :: c31:c32
const3 :: c20
const4 :: c22
const5 :: c26
const6 :: c50
const7 :: c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
const8 :: c28
const9 :: c2
const10 :: c40
const11 :: c6
const12 :: c43:c44
const13 :: c34:c36
const14 :: c10
const15 :: c47

Rewrite Strategy: INNERMOST
----------------------------------------

(33) NarrowingProof (BOTH BOUNDS(ID, ID))
Narrowed the inner basic terms of all right-hand sides by a single narrowing step.
----------------------------------------

(34)
Obligation:
Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:

Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   A__U41(tt, 0, z1) -> c14(A__U42(tt, z1), A__ISNAT(0)) [1]
   A__U41(tt, length(z0'), z1) -> c14(A__U42(a__U11(a__isNatIListKind(z0'), z0'), z1), A__ISNAT(length(z0'))) [1]
   A__U41(tt, s(z0''), z1) -> c14(A__U42(a__U21(a__isNatKind(z0''), z0''), z1), A__ISNAT(s(z0''))) [1]
   A__U41(tt, z0, z1) -> c14(A__U42(isNat(z0), z1), A__ISNAT(z0)) [1]
   A__U41(tt, z0, z1) -> c14(A__U42(null_a__isNat, z1), A__ISNAT(z0)) [1]
   A__U51(tt, 0, z1) -> c20(A__U52(tt, z1), A__ISNAT(0)) [1]
   A__U51(tt, length(z01), z1) -> c20(A__U52(a__U11(a__isNatIListKind(z01), z01), z1), A__ISNAT(length(z01))) [1]
   A__U51(tt, s(z02), z1) -> c20(A__U52(a__U21(a__isNatKind(z02), z02), z1), A__ISNAT(s(z02))) [1]
   A__U51(tt, z0, z1) -> c20(A__U52(isNat(z0), z1), A__ISNAT(z0)) [1]
   A__U51(tt, z0, z1) -> c20(A__U52(null_a__isNat, z1), A__ISNAT(z0)) [1]
   A__U61(tt, z0) -> c26(A__LENGTH(mark(z0)), MARK(z0)) [1]
   A__AND(tt, z0) -> c28(MARK(z0)) [1]
   A__ISNAT(length(nil)) -> c31(A__U11(tt, nil), A__ISNATILISTKIND(nil)) [1]
   A__ISNAT(length(zeros)) -> c31(A__U11(tt, zeros), A__ISNATILISTKIND(zeros)) [1]
   A__ISNAT(length(cons(z025, z19))) -> c31(A__U11(a__and(a__isNatKind(z025), isNatIListKind(z19)), cons(z025, z19)), A__ISNATILISTKIND(cons(z025, z19))) [1]
   A__ISNAT(length(z0)) -> c31(A__U11(isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) [1]
   A__ISNAT(length(z0)) -> c31(A__U11(null_a__isNatIListKind, z0), A__ISNATILISTKIND(z0)) [1]
   A__ISNAT(s(0)) -> c32(A__U21(tt, 0), A__ISNATKIND(0)) [1]
   A__ISNAT(s(length(z026))) -> c32(A__U21(a__isNatIListKind(z026), length(z026)), A__ISNATKIND(length(z026))) [1]
   A__ISNAT(s(s(z027))) -> c32(A__U21(a__isNatKind(z027), s(z027)), A__ISNATKIND(s(z027))) [1]
   A__ISNAT(s(z0)) -> c32(A__U21(isNatKind(z0), z0), A__ISNATKIND(z0)) [1]
   A__ISNAT(s(z0)) -> c32(A__U21(null_a__isNatKind, z0), A__ISNATKIND(z0)) [1]
   A__ISNATILIST(nil) -> c34(A__U31(tt, nil), A__ISNATILISTKIND(nil)) [1]
   A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros), A__ISNATILISTKIND(zeros)) [1]
   A__ISNATILIST(cons(z028, z110)) -> c34(A__U31(a__and(a__isNatKind(z028), isNatIListKind(z110)), cons(z028, z110)), A__ISNATILISTKIND(cons(z028, z110))) [1]
   A__ISNATILIST(z0) -> c34(A__U31(isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) [1]
   A__ISNATILIST(z0) -> c34(A__U31(null_a__isNatIListKind, z0), A__ISNATILISTKIND(z0)) [1]
   A__ISNATILIST(cons(0, z1)) -> c36(A__U41(a__and(tt, isNatIListKind(z1)), 0, z1), A__AND(tt, isNatIListKind(z1)), A__ISNATKIND(0)) [1]
   A__ISNATILIST(cons(0, z1)) -> c36(A__U41(a__and(tt, isNatIListKind(z1)), 0, z1), A__AND(isNatKind(0), isNatIListKind(z1)), A__ISNATKIND(0)) [1]
   A__ISNATILIST(cons(0, z1)) -> c36(A__U41(a__and(tt, isNatIListKind(z1)), 0, z1), A__AND(null_a__isNatKind, isNatIListKind(z1)), A__ISNATKIND(0)) [1]
   A__ISNATILIST(cons(length(z029), z1)) -> c36(A__U41(a__and(a__isNatIListKind(z029), isNatIListKind(z1)), length(z029), z1), A__AND(a__isNatIListKind(z029), isNatIListKind(z1)), A__ISNATKIND(length(z029))) [1]
   A__ISNATILIST(cons(length(z029), z1)) -> c36(A__U41(a__and(a__isNatIListKind(z029), isNatIListKind(z1)), length(z029), z1), A__AND(isNatKind(length(z029)), isNatIListKind(z1)), A__ISNATKIND(length(z029))) [1]
   A__ISNATILIST(cons(length(z029), z1)) -> c36(A__U41(a__and(a__isNatIListKind(z029), isNatIListKind(z1)), length(z029), z1), A__AND(null_a__isNatKind, isNatIListKind(z1)), A__ISNATKIND(length(z029))) [1]
   A__ISNATILIST(cons(s(z030), z1)) -> c36(A__U41(a__and(a__isNatKind(z030), isNatIListKind(z1)), s(z030), z1), A__AND(a__isNatKind(z030), isNatIListKind(z1)), A__ISNATKIND(s(z030))) [1]
   A__ISNATILIST(cons(s(z030), z1)) -> c36(A__U41(a__and(a__isNatKind(z030), isNatIListKind(z1)), s(z030), z1), A__AND(isNatKind(s(z030)), isNatIListKind(z1)), A__ISNATKIND(s(z030))) [1]
   A__ISNATILIST(cons(s(z030), z1)) -> c36(A__U41(a__and(a__isNatKind(z030), isNatIListKind(z1)), s(z030), z1), A__AND(null_a__isNatKind, isNatIListKind(z1)), A__ISNATKIND(s(z030))) [1]
   A__ISNATILIST(cons(0, z1)) -> c36(A__U41(a__and(isNatKind(0), isNatIListKind(z1)), 0, z1), A__AND(tt, isNatIListKind(z1)), A__ISNATKIND(0)) [1]
   A__ISNATILIST(cons(length(z031), z1)) -> c36(A__U41(a__and(isNatKind(length(z031)), isNatIListKind(z1)), length(z031), z1), A__AND(a__isNatIListKind(z031), isNatIListKind(z1)), A__ISNATKIND(length(z031))) [1]
   A__ISNATILIST(cons(s(z032), z1)) -> c36(A__U41(a__and(isNatKind(s(z032)), isNatIListKind(z1)), s(z032), z1), A__AND(a__isNatKind(z032), isNatIListKind(z1)), A__ISNATKIND(s(z032))) [1]
   A__ISNATILIST(cons(z0, z1)) -> c36(A__U41(a__and(isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) [1]
   A__ISNATILIST(cons(z0, z1)) -> c36(A__U41(a__and(isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(null_a__isNatKind, isNatIListKind(z1)), A__ISNATKIND(z0)) [1]
   A__ISNATILIST(cons(0, z1)) -> c36(A__U41(a__and(null_a__isNatKind, isNatIListKind(z1)), 0, z1), A__AND(tt, isNatIListKind(z1)), A__ISNATKIND(0)) [1]
   A__ISNATILIST(cons(length(z033), z1)) -> c36(A__U41(a__and(null_a__isNatKind, isNatIListKind(z1)), length(z033), z1), A__AND(a__isNatIListKind(z033), isNatIListKind(z1)), A__ISNATKIND(length(z033))) [1]
   A__ISNATILIST(cons(s(z034), z1)) -> c36(A__U41(a__and(null_a__isNatKind, isNatIListKind(z1)), s(z034), z1), A__AND(a__isNatKind(z034), isNatIListKind(z1)), A__ISNATKIND(s(z034))) [1]
   A__ISNATILIST(cons(z0, z1)) -> c36(A__U41(a__and(null_a__isNatKind, isNatIListKind(z1)), z0, z1), A__AND(isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) [1]
   A__ISNATILIST(cons(z0, z1)) -> c36(A__U41(a__and(null_a__isNatKind, isNatIListKind(z1)), z0, z1), A__AND(null_a__isNatKind, isNatIListKind(z1)), A__ISNATKIND(z0)) [1]
   A__ISNATILISTKIND(cons(0, z1)) -> c40(A__AND(tt, isNatIListKind(z1)), A__ISNATKIND(0)) [1]
   A__ISNATILISTKIND(cons(length(z035), z1)) -> c40(A__AND(a__isNatIListKind(z035), isNatIListKind(z1)), A__ISNATKIND(length(z035))) [1]
   A__ISNATILISTKIND(cons(s(z036), z1)) -> c40(A__AND(a__isNatKind(z036), isNatIListKind(z1)), A__ISNATKIND(s(z036))) [1]
   A__ISNATILISTKIND(cons(z0, z1)) -> c40(A__AND(isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) [1]
   A__ISNATILISTKIND(cons(z0, z1)) -> c40(A__AND(null_a__isNatKind, isNatIListKind(z1)), A__ISNATKIND(z0)) [1]
   A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) [1]
   A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) [1]
   A__ISNATLIST(cons(0, z1)) -> c47(A__U51(a__and(tt, isNatIListKind(z1)), 0, z1), A__AND(tt, isNatIListKind(z1)), A__ISNATKIND(0)) [1]
   A__ISNATLIST(cons(0, z1)) -> c47(A__U51(a__and(tt, isNatIListKind(z1)), 0, z1), A__AND(isNatKind(0), isNatIListKind(z1)), A__ISNATKIND(0)) [1]
   A__ISNATLIST(cons(0, z1)) -> c47(A__U51(a__and(tt, isNatIListKind(z1)), 0, z1), A__AND(null_a__isNatKind, isNatIListKind(z1)), A__ISNATKIND(0)) [1]
   A__ISNATLIST(cons(length(z037), z1)) -> c47(A__U51(a__and(a__isNatIListKind(z037), isNatIListKind(z1)), length(z037), z1), A__AND(a__isNatIListKind(z037), isNatIListKind(z1)), A__ISNATKIND(length(z037))) [1]
   A__ISNATLIST(cons(length(z037), z1)) -> c47(A__U51(a__and(a__isNatIListKind(z037), isNatIListKind(z1)), length(z037), z1), A__AND(isNatKind(length(z037)), isNatIListKind(z1)), A__ISNATKIND(length(z037))) [1]
   A__ISNATLIST(cons(length(z037), z1)) -> c47(A__U51(a__and(a__isNatIListKind(z037), isNatIListKind(z1)), length(z037), z1), A__AND(null_a__isNatKind, isNatIListKind(z1)), A__ISNATKIND(length(z037))) [1]
   A__ISNATLIST(cons(s(z038), z1)) -> c47(A__U51(a__and(a__isNatKind(z038), isNatIListKind(z1)), s(z038), z1), A__AND(a__isNatKind(z038), isNatIListKind(z1)), A__ISNATKIND(s(z038))) [1]
   A__ISNATLIST(cons(s(z038), z1)) -> c47(A__U51(a__and(a__isNatKind(z038), isNatIListKind(z1)), s(z038), z1), A__AND(isNatKind(s(z038)), isNatIListKind(z1)), A__ISNATKIND(s(z038))) [1]
   A__ISNATLIST(cons(s(z038), z1)) -> c47(A__U51(a__and(a__isNatKind(z038), isNatIListKind(z1)), s(z038), z1), A__AND(null_a__isNatKind, isNatIListKind(z1)), A__ISNATKIND(s(z038))) [1]
   A__ISNATLIST(cons(0, z1)) -> c47(A__U51(a__and(isNatKind(0), isNatIListKind(z1)), 0, z1), A__AND(tt, isNatIListKind(z1)), A__ISNATKIND(0)) [1]
   A__ISNATLIST(cons(length(z039), z1)) -> c47(A__U51(a__and(isNatKind(length(z039)), isNatIListKind(z1)), length(z039), z1), A__AND(a__isNatIListKind(z039), isNatIListKind(z1)), A__ISNATKIND(length(z039))) [1]
   A__ISNATLIST(cons(s(z040), z1)) -> c47(A__U51(a__and(isNatKind(s(z040)), isNatIListKind(z1)), s(z040), z1), A__AND(a__isNatKind(z040), isNatIListKind(z1)), A__ISNATKIND(s(z040))) [1]
   A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) [1]
   A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(null_a__isNatKind, isNatIListKind(z1)), A__ISNATKIND(z0)) [1]
   A__ISNATLIST(cons(0, z1)) -> c47(A__U51(a__and(null_a__isNatKind, isNatIListKind(z1)), 0, z1), A__AND(tt, isNatIListKind(z1)), A__ISNATKIND(0)) [1]
   A__ISNATLIST(cons(length(z041), z1)) -> c47(A__U51(a__and(null_a__isNatKind, isNatIListKind(z1)), length(z041), z1), A__AND(a__isNatIListKind(z041), isNatIListKind(z1)), A__ISNATKIND(length(z041))) [1]
   A__ISNATLIST(cons(s(z042), z1)) -> c47(A__U51(a__and(null_a__isNatKind, isNatIListKind(z1)), s(z042), z1), A__AND(a__isNatKind(z042), isNatIListKind(z1)), A__ISNATKIND(s(z042))) [1]
   A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(null_a__isNatKind, isNatIListKind(z1)), z0, z1), A__AND(isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) [1]
   A__ISNATLIST(cons(z0, z1)) -> c47(A__U51(a__and(null_a__isNatKind, isNatIListKind(z1)), z0, z1), A__AND(null_a__isNatKind, isNatIListKind(z1)), A__ISNATKIND(z0)) [1]
   A__LENGTH(cons(z0, z1)) -> 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)) [1]
   MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) [1]
   MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) [1]
   MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) [1]
   MARK(isNat(z0)) -> c58(A__ISNAT(z0)) [1]
   MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) [1]
   MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) [1]
   MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) [1]
   MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) [1]
   MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) [1]
   MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) [1]
   MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) [1]
   MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) [1]
   MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) [1]
   MARK(cons(z0, z1)) -> c73(MARK(z0)) [1]
   MARK(s(z0)) -> c76(MARK(z0)) [1]
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) [1]
   A__U21(tt, z0) -> c6(A__ISNAT(z0)) [1]
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) [1]
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) [1]
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) [1]
   MARK(U12(z0)) -> c54(MARK(z0)) [1]
   MARK(U22(z0)) -> c57(MARK(z0)) [1]
   MARK(U32(z0)) -> c60(MARK(z0)) [1]
   MARK(U43(z0)) -> c63(MARK(z0)) [1]
   MARK(U53(z0)) -> c67(MARK(z0)) [1]
   a__zeros -> cons(0, zeros) [0]
   a__zeros -> zeros [0]
   a__U11(tt, nil) -> a__U12(tt) [0]
   a__U11(tt, cons(z0270, z1118)) -> a__U12(a__U51(a__and(a__isNatKind(z0270), isNatIListKind(z1118)), z0270, z1118)) [0]
   a__U11(tt, z0) -> a__U12(isNatList(z0)) [0]
   a__U11(tt, z0) -> a__U12(null_a__isNatList) [0]
   a__U11(z0, z1) -> U11(z0, z1) [0]
   a__U12(tt) -> tt [0]
   a__U12(z0) -> U12(z0) [0]
   a__U21(tt, 0) -> a__U22(tt) [0]
   a__U21(tt, length(z0271)) -> a__U22(a__U11(a__isNatIListKind(z0271), z0271)) [0]
   a__U21(tt, s(z0272)) -> a__U22(a__U21(a__isNatKind(z0272), z0272)) [0]
   a__U21(tt, z0) -> a__U22(isNat(z0)) [0]
   a__U21(tt, z0) -> a__U22(null_a__isNat) [0]
   a__U21(z0, z1) -> U21(z0, z1) [0]
   a__U22(tt) -> tt [0]
   a__U22(z0) -> U22(z0) [0]
   a__U31(tt, nil) -> a__U32(tt) [0]
   a__U31(tt, cons(z0273, z1119)) -> a__U32(a__U51(a__and(a__isNatKind(z0273), isNatIListKind(z1119)), z0273, z1119)) [0]
   a__U31(tt, z0) -> a__U32(isNatList(z0)) [0]
   a__U31(tt, z0) -> a__U32(null_a__isNatList) [0]
   a__U31(z0, z1) -> U31(z0, z1) [0]
   a__U32(tt) -> tt [0]
   a__U32(z0) -> U32(z0) [0]
   a__U41(tt, 0, z1) -> a__U42(tt, z1) [0]
   a__U41(tt, length(z0274), z1) -> a__U42(a__U11(a__isNatIListKind(z0274), z0274), z1) [0]
   a__U41(tt, s(z0275), z1) -> a__U42(a__U21(a__isNatKind(z0275), z0275), z1) [0]
   a__U41(tt, z0, z1) -> a__U42(isNat(z0), z1) [0]
   a__U41(tt, z0, z1) -> a__U42(null_a__isNat, z1) [0]
   a__U41(z0, z1, z2) -> U41(z0, z1, z2) [0]
   a__U42(tt, z0) -> a__U43(a__U31(a__isNatIListKind(z0), z0)) [0]
   a__U42(tt, zeros) -> a__U43(tt) [0]
   a__U42(tt, cons(z0276, z1120)) -> a__U43(a__U41(a__and(a__isNatKind(z0276), isNatIListKind(z1120)), z0276, z1120)) [0]
   a__U42(tt, z0) -> a__U43(isNatIList(z0)) [0]
   a__U42(tt, z0) -> a__U43(null_a__isNatIList) [0]
   a__U42(z0, z1) -> U42(z0, z1) [0]
   a__U43(tt) -> tt [0]
   a__U43(z0) -> U43(z0) [0]
   a__U51(tt, 0, z1) -> a__U52(tt, z1) [0]
   a__U51(tt, length(z0277), z1) -> a__U52(a__U11(a__isNatIListKind(z0277), z0277), z1) [0]
   a__U51(tt, s(z0278), z1) -> a__U52(a__U21(a__isNatKind(z0278), z0278), z1) [0]
   a__U51(tt, z0, z1) -> a__U52(isNat(z0), z1) [0]
   a__U51(tt, z0, z1) -> a__U52(null_a__isNat, z1) [0]
   a__U51(z0, z1, z2) -> U51(z0, z1, z2) [0]
   a__U52(tt, nil) -> a__U53(tt) [0]
   a__U52(tt, cons(z0279, z1121)) -> a__U53(a__U51(a__and(a__isNatKind(z0279), isNatIListKind(z1121)), z0279, z1121)) [0]
   a__U52(tt, z0) -> a__U53(isNatList(z0)) [0]
   a__U52(tt, z0) -> a__U53(null_a__isNatList) [0]
   a__U52(z0, z1) -> U52(z0, z1) [0]
   a__U53(tt) -> tt [0]
   a__U53(z0) -> U53(z0) [0]
   a__U61(tt, z0) -> s(a__length(mark(z0))) [0]
   a__U61(z0, z1) -> U61(z0, z1) [0]
   a__and(tt, z0) -> mark(z0) [0]
   a__and(z0, z1) -> and(z0, z1) [0]
   a__isNat(0) -> tt [0]
   a__isNat(length(nil)) -> a__U11(tt, nil) [0]
   a__isNat(length(zeros)) -> a__U11(tt, zeros) [0]
   a__isNat(length(cons(z0302, z1132))) -> a__U11(a__and(a__isNatKind(z0302), isNatIListKind(z1132)), cons(z0302, z1132)) [0]
   a__isNat(length(z0)) -> a__U11(isNatIListKind(z0), z0) [0]
   a__isNat(length(z0)) -> a__U11(null_a__isNatIListKind, z0) [0]
   a__isNat(s(0)) -> a__U21(tt, 0) [0]
   a__isNat(s(length(z0303))) -> a__U21(a__isNatIListKind(z0303), length(z0303)) [0]
   a__isNat(s(s(z0304))) -> a__U21(a__isNatKind(z0304), s(z0304)) [0]
   a__isNat(s(z0)) -> a__U21(isNatKind(z0), z0) [0]
   a__isNat(s(z0)) -> a__U21(null_a__isNatKind, z0) [0]
   a__isNat(z0) -> isNat(z0) [0]
   a__isNatIList(nil) -> a__U31(tt, nil) [0]
   a__isNatIList(zeros) -> a__U31(tt, zeros) [0]
   a__isNatIList(cons(z0305, z1133)) -> a__U31(a__and(a__isNatKind(z0305), isNatIListKind(z1133)), cons(z0305, z1133)) [0]
   a__isNatIList(z0) -> a__U31(isNatIListKind(z0), z0) [0]
   a__isNatIList(z0) -> a__U31(null_a__isNatIListKind, z0) [0]
   a__isNatIList(zeros) -> tt [0]
   a__isNatIList(cons(0, z1)) -> a__U41(a__and(tt, isNatIListKind(z1)), 0, z1) [0]
   a__isNatIList(cons(length(z0306), z1)) -> a__U41(a__and(a__isNatIListKind(z0306), isNatIListKind(z1)), length(z0306), z1) [0]
   a__isNatIList(cons(s(z0307), z1)) -> a__U41(a__and(a__isNatKind(z0307), isNatIListKind(z1)), s(z0307), z1) [0]
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(isNatKind(z0), isNatIListKind(z1)), z0, z1) [0]
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(null_a__isNatKind, isNatIListKind(z1)), z0, z1) [0]
   a__isNatIList(z0) -> isNatIList(z0) [0]
   a__isNatIListKind(nil) -> tt [0]
   a__isNatIListKind(zeros) -> tt [0]
   a__isNatIListKind(cons(0, z1)) -> a__and(tt, isNatIListKind(z1)) [0]
   a__isNatIListKind(cons(length(z0308), z1)) -> a__and(a__isNatIListKind(z0308), isNatIListKind(z1)) [0]
   a__isNatIListKind(cons(s(z0309), z1)) -> a__and(a__isNatKind(z0309), isNatIListKind(z1)) [0]
   a__isNatIListKind(cons(z0, z1)) -> a__and(isNatKind(z0), isNatIListKind(z1)) [0]
   a__isNatIListKind(cons(z0, z1)) -> a__and(null_a__isNatKind, isNatIListKind(z1)) [0]
   a__isNatIListKind(z0) -> isNatIListKind(z0) [0]
   a__isNatKind(0) -> tt [0]
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0) [0]
   a__isNatKind(s(z0)) -> a__isNatKind(z0) [0]
   a__isNatKind(z0) -> isNatKind(z0) [0]
   a__isNatList(nil) -> tt [0]
   a__isNatList(cons(0, z1)) -> a__U51(a__and(tt, isNatIListKind(z1)), 0, z1) [0]
   a__isNatList(cons(length(z0310), z1)) -> a__U51(a__and(a__isNatIListKind(z0310), isNatIListKind(z1)), length(z0310), z1) [0]
   a__isNatList(cons(s(z0311), z1)) -> a__U51(a__and(a__isNatKind(z0311), isNatIListKind(z1)), s(z0311), z1) [0]
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(isNatKind(z0), isNatIListKind(z1)), z0, z1) [0]
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(null_a__isNatKind, isNatIListKind(z1)), z0, z1) [0]
   a__isNatList(z0) -> isNatList(z0) [0]
   a__length(nil) -> 0 [0]
   a__length(cons(z0, nil)) -> a__U61(a__and(a__and(tt, isNatIListKind(nil)), and(isNat(z0), isNatKind(z0))), nil) [0]
   a__length(cons(z0, cons(z0312, z1134))) -> a__U61(a__and(a__and(a__U51(a__and(a__isNatKind(z0312), isNatIListKind(z1134)), z0312, z1134), isNatIListKind(cons(z0312, z1134))), and(isNat(z0), isNatKind(z0))), cons(z0312, z1134)) [0]
   a__length(cons(z0, z1)) -> a__U61(a__and(a__and(isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) [0]
   a__length(cons(z0, z1)) -> a__U61(a__and(a__and(null_a__isNatList, isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) [0]
   a__length(z0) -> length(z0) [0]
   mark(zeros) -> a__zeros [0]
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1) [0]
   mark(U12(z0)) -> a__U12(mark(z0)) [0]
   mark(isNatList(z0)) -> a__isNatList(z0) [0]
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1) [0]
   mark(U22(z0)) -> a__U22(mark(z0)) [0]
   mark(isNat(z0)) -> a__isNat(z0) [0]
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1) [0]
   mark(U32(z0)) -> a__U32(mark(z0)) [0]
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) [0]
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1) [0]
   mark(U43(z0)) -> a__U43(mark(z0)) [0]
   mark(isNatIList(z0)) -> a__isNatIList(z0) [0]
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) [0]
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1) [0]
   mark(U53(z0)) -> a__U53(mark(z0)) [0]
   mark(U61(z0, z1)) -> a__U61(mark(z0), z1) [0]
   mark(length(z0)) -> a__length(mark(z0)) [0]
   mark(and(z0, z1)) -> a__and(mark(z0), z1) [0]
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) [0]
   mark(isNatKind(z0)) -> a__isNatKind(z0) [0]
   mark(cons(z0, z1)) -> cons(mark(z0), z1) [0]
   mark(0) -> 0 [0]
   mark(tt) -> tt [0]
   mark(s(z0)) -> s(mark(z0)) [0]
   mark(nil) -> nil [0]
   a__zeros -> null_a__zeros [0]
   a__U11(v0, v1) -> null_a__U11 [0]
   a__U12(v0) -> null_a__U12 [0]
   a__U21(v0, v1) -> null_a__U21 [0]
   a__U22(v0) -> null_a__U22 [0]
   a__U31(v0, v1) -> null_a__U31 [0]
   a__U32(v0) -> null_a__U32 [0]
   a__U41(v0, v1, v2) -> null_a__U41 [0]
   a__U42(v0, v1) -> null_a__U42 [0]
   a__U43(v0) -> null_a__U43 [0]
   a__U51(v0, v1, v2) -> null_a__U51 [0]
   a__U52(v0, v1) -> null_a__U52 [0]
   a__U53(v0) -> null_a__U53 [0]
   a__U61(v0, v1) -> null_a__U61 [0]
   a__and(v0, v1) -> null_a__and [0]
   a__isNat(v0) -> null_a__isNat [0]
   a__isNatIList(v0) -> null_a__isNatIList [0]
   a__isNatIListKind(v0) -> null_a__isNatIListKind [0]
   a__isNatKind(v0) -> null_a__isNatKind [0]
   a__isNatList(v0) -> null_a__isNatList [0]
   a__length(v0) -> null_a__length [0]
   mark(v0) -> null_mark [0]

The TRS has the following type information:
A__U41 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c14
tt :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c14 :: c16 -> c31:c32 -> c14
A__U42 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c16
a__isNat :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
A__ISNAT :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c31:c32
A__U51 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c20
c20 :: c22 -> c31:c32 -> c20
A__U52 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c22
A__U61 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c26
c26 :: c50 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c26
A__LENGTH :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c50
mark :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
MARK :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
A__AND :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c28
c28 :: c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c28
length :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c31 :: c2 -> c40 -> c31:c32
A__U11 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c2
a__isNatIListKind :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
A__ISNATILISTKIND :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c40
s :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c32 :: c6 -> c43:c44 -> c31:c32
A__U21 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c6
a__isNatKind :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
A__ISNATKIND :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c43:c44
A__ISNATILIST :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c34:c36
c34 :: c10 -> c40 -> c34:c36
A__U31 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c10
cons :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c36 :: c14 -> c28 -> c43:c44 -> c34:c36
a__and :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
isNatIListKind :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c40 :: c28 -> c43:c44 -> c40
c43 :: c40 -> c43:c44
c44 :: c43:c44 -> c43:c44
A__ISNATLIST :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c47
c47 :: c20 -> c28 -> c43:c44 -> c47
c50 :: c26 -> c28 -> c28 -> c47 -> c50
a__isNatList :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
and :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
isNat :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
isNatKind :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
U11 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c53 :: c2 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
isNatList :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c55 :: c47 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
U21 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c56 :: c6 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
c58 :: c31:c32 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
U31 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c59 :: c10 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
U41 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c61 :: c14 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
U42 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c62 :: c16 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
isNatIList :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c64 :: c34:c36 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
U51 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c65 :: c20 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
U52 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c66 :: c22 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
U61 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c68 :: c26 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
c69 :: c50 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
c70 :: c28 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
c71 :: c40 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
c72 :: c43:c44 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
c73 :: c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
c76 :: c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
c2 :: c47 -> c2
c6 :: c31:c32 -> c6
c10 :: c47 -> c10
c16 :: c34:c36 -> c16
c22 :: c47 -> c22
U12 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c54 :: c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
U22 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c57 :: c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
U32 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c60 :: c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
U43 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c63 :: c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
U53 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c67 :: c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
a__zeros :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
0 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
zeros :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__U11 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__U12 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__U21 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__U22 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__U31 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__U32 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__U41 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__U42 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__U43 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__isNatIList :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__U51 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__U52 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__U53 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__U61 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__length :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
nil :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__zeros :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__U11 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__U12 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__U21 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__U22 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__U31 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__U32 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__U41 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__U42 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__U43 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__U51 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__U52 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__U53 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__U61 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__and :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__isNat :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__isNatIList :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__isNatIListKind :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__isNatKind :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__isNatList :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__length :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_mark :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
const :: c14
const1 :: c16
const2 :: c31:c32
const3 :: c20
const4 :: c22
const5 :: c26
const6 :: c50
const7 :: c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67
const8 :: c28
const9 :: c2
const10 :: c40
const11 :: c6
const12 :: c43:c44
const13 :: c34:c36
const14 :: c10
const15 :: c47

Rewrite Strategy: INNERMOST
----------------------------------------

(35) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID))
Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction.
The constant constructors are abstracted as follows:

   tt => 2
   0 => 0
   zeros => 3
   nil => 1
   null_a__zeros => 0
   null_a__U11 => 0
   null_a__U12 => 0
   null_a__U21 => 0
   null_a__U22 => 0
   null_a__U31 => 0
   null_a__U32 => 0
   null_a__U41 => 0
   null_a__U42 => 0
   null_a__U43 => 0
   null_a__U51 => 0
   null_a__U52 => 0
   null_a__U53 => 0
   null_a__U61 => 0
   null_a__and => 0
   null_a__isNat => 0
   null_a__isNatIList => 0
   null_a__isNatIListKind => 0
   null_a__isNatKind => 0
   null_a__isNatList => 0
   null_a__length => 0
   null_mark => 0
   const => 0
   const1 => 0
   const2 => 0
   const3 => 0
   const4 => 0
   const5 => 0
   const6 => 0
   const7 => 0
   const8 => 0
   const9 => 0
   const10 => 0
   const11 => 0
   const12 => 0
   const13 => 0
   const14 => 0
   const15 => 0

----------------------------------------

(36)
Obligation:
Complexity RNTS consisting of the following rules:

   A__AND(z, z') -{ 1 }-> 1 + MARK(z0) :|: z = 2, z0 >= 0, z' = z0
   A__ISNAT(z) -{ 1 }-> 1 + A__U21(a__isNatKind(z027), 1 + z027) + A__ISNATKIND(1 + z027) :|: z027 >= 0, z = 1 + (1 + z027)
   A__ISNAT(z) -{ 1 }-> 1 + A__U21(a__isNatIListKind(z026), 1 + z026) + A__ISNATKIND(1 + z026) :|: z = 1 + (1 + z026), z026 >= 0
   A__ISNAT(z) -{ 1 }-> 1 + A__U21(2, 0) + A__ISNATKIND(0) :|: z = 1 + 0
   A__ISNAT(z) -{ 1 }-> 1 + A__U21(0, z0) + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0
   A__ISNAT(z) -{ 1 }-> 1 + A__U21(1 + z0, z0) + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0
   A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(a__isNatKind(z025), 1 + z19), 1 + z025 + z19) + A__ISNATILISTKIND(1 + z025 + z19) :|: z025 >= 0, z = 1 + (1 + z025 + z19), z19 >= 0
   A__ISNAT(z) -{ 1 }-> 1 + A__U11(2, 3) + A__ISNATILISTKIND(3) :|: z = 1 + 3
   A__ISNAT(z) -{ 1 }-> 1 + A__U11(2, 1) + A__ISNATILISTKIND(1) :|: z = 1 + 1
   A__ISNAT(z) -{ 1 }-> 1 + A__U11(0, z0) + A__ISNATILISTKIND(z0) :|: z = 1 + z0, z0 >= 0
   A__ISNAT(z) -{ 1 }-> 1 + A__U11(1 + z0, z0) + A__ISNATILISTKIND(z0) :|: z = 1 + z0, z0 >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U31(a__and(a__isNatKind(z028), 1 + z110), 1 + z028 + z110) + A__ISNATILISTKIND(1 + z028 + z110) :|: z110 >= 0, z = 1 + z028 + z110, z028 >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U31(2, 3) + A__ISNATILISTKIND(3) :|: z = 3
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U31(2, 1) + A__ISNATILISTKIND(1) :|: z = 1
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U31(0, z0) + A__ISNATILISTKIND(z0) :|: z = z0, z0 >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U31(1 + z0, z0) + A__ISNATILISTKIND(z0) :|: z = z0, z0 >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(a__isNatKind(z030), 1 + z1), 1 + z030, z1) + A__AND(a__isNatKind(z030), 1 + z1) + A__ISNATKIND(1 + z030) :|: z1 >= 0, z = 1 + (1 + z030) + z1, z030 >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(a__isNatKind(z030), 1 + z1), 1 + z030, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(1 + z030) :|: z1 >= 0, z = 1 + (1 + z030) + z1, z030 >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(a__isNatKind(z030), 1 + z1), 1 + z030, z1) + A__AND(1 + (1 + z030), 1 + z1) + A__ISNATKIND(1 + z030) :|: z1 >= 0, z = 1 + (1 + z030) + z1, z030 >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(a__isNatIListKind(z029), 1 + z1), 1 + z029, z1) + A__AND(a__isNatIListKind(z029), 1 + z1) + A__ISNATKIND(1 + z029) :|: z029 >= 0, z = 1 + (1 + z029) + z1, z1 >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(a__isNatIListKind(z029), 1 + z1), 1 + z029, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(1 + z029) :|: z029 >= 0, z = 1 + (1 + z029) + z1, z1 >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(a__isNatIListKind(z029), 1 + z1), 1 + z029, z1) + A__AND(1 + (1 + z029), 1 + z1) + A__ISNATKIND(1 + z029) :|: z029 >= 0, z = 1 + (1 + z029) + z1, z1 >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(2, 1 + z1), 0, z1) + A__AND(2, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(2, 1 + z1), 0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(2, 1 + z1), 0, z1) + A__AND(1 + 0, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(0, 1 + z1), z0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(0, 1 + z1), z0, z1) + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(0, 1 + z1), 0, z1) + A__AND(2, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(0, 1 + z1), 1 + z033, z1) + A__AND(a__isNatIListKind(z033), 1 + z1) + A__ISNATKIND(1 + z033) :|: z1 >= 0, z = 1 + (1 + z033) + z1, z033 >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(0, 1 + z1), 1 + z034, z1) + A__AND(a__isNatKind(z034), 1 + z1) + A__ISNATKIND(1 + z034) :|: z1 >= 0, z034 >= 0, z = 1 + (1 + z034) + z1
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(1 + z0, 1 + z1), z0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(1 + z0, 1 + z1), z0, z1) + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(1 + 0, 1 + z1), 0, z1) + A__AND(2, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(1 + (1 + z031), 1 + z1), 1 + z031, z1) + A__AND(a__isNatIListKind(z031), 1 + z1) + A__ISNATKIND(1 + z031) :|: z = 1 + (1 + z031) + z1, z031 >= 0, z1 >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(1 + (1 + z032), 1 + z1), 1 + z032, z1) + A__AND(a__isNatKind(z032), 1 + z1) + A__ISNATKIND(1 + z032) :|: z032 >= 0, z1 >= 0, z = 1 + (1 + z032) + z1
   A__ISNATILISTKIND(z) -{ 1 }-> 1 + A__AND(a__isNatKind(z036), 1 + z1) + A__ISNATKIND(1 + z036) :|: z036 >= 0, z1 >= 0, z = 1 + (1 + z036) + z1
   A__ISNATILISTKIND(z) -{ 1 }-> 1 + A__AND(a__isNatIListKind(z035), 1 + z1) + A__ISNATKIND(1 + z035) :|: z035 >= 0, z1 >= 0, z = 1 + (1 + z035) + z1
   A__ISNATILISTKIND(z) -{ 1 }-> 1 + A__AND(2, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1
   A__ISNATILISTKIND(z) -{ 1 }-> 1 + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__ISNATILISTKIND(z) -{ 1 }-> 1 + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__ISNATKIND(z) -{ 1 }-> 1 + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0
   A__ISNATKIND(z) -{ 1 }-> 1 + A__ISNATILISTKIND(z0) :|: z = 1 + z0, z0 >= 0
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(a__isNatKind(z038), 1 + z1), 1 + z038, z1) + A__AND(a__isNatKind(z038), 1 + z1) + A__ISNATKIND(1 + z038) :|: z1 >= 0, z = 1 + (1 + z038) + z1, z038 >= 0
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(a__isNatKind(z038), 1 + z1), 1 + z038, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(1 + z038) :|: z1 >= 0, z = 1 + (1 + z038) + z1, z038 >= 0
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(a__isNatKind(z038), 1 + z1), 1 + z038, z1) + A__AND(1 + (1 + z038), 1 + z1) + A__ISNATKIND(1 + z038) :|: z1 >= 0, z = 1 + (1 + z038) + z1, z038 >= 0
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(a__isNatIListKind(z037), 1 + z1), 1 + z037, z1) + A__AND(a__isNatIListKind(z037), 1 + z1) + A__ISNATKIND(1 + z037) :|: z1 >= 0, z = 1 + (1 + z037) + z1, z037 >= 0
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(a__isNatIListKind(z037), 1 + z1), 1 + z037, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(1 + z037) :|: z1 >= 0, z = 1 + (1 + z037) + z1, z037 >= 0
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(a__isNatIListKind(z037), 1 + z1), 1 + z037, z1) + A__AND(1 + (1 + z037), 1 + z1) + A__ISNATKIND(1 + z037) :|: z1 >= 0, z = 1 + (1 + z037) + z1, z037 >= 0
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(2, 1 + z1), 0, z1) + A__AND(2, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(2, 1 + z1), 0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(2, 1 + z1), 0, z1) + A__AND(1 + 0, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(0, 1 + z1), z0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(0, 1 + z1), z0, z1) + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(0, 1 + z1), 0, z1) + A__AND(2, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(0, 1 + z1), 1 + z041, z1) + A__AND(a__isNatIListKind(z041), 1 + z1) + A__ISNATKIND(1 + z041) :|: z1 >= 0, z041 >= 0, z = 1 + (1 + z041) + z1
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(0, 1 + z1), 1 + z042, z1) + A__AND(a__isNatKind(z042), 1 + z1) + A__ISNATKIND(1 + z042) :|: z042 >= 0, z1 >= 0, z = 1 + (1 + z042) + z1
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(1 + z0, 1 + z1), z0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(1 + z0, 1 + z1), z0, z1) + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(1 + 0, 1 + z1), 0, z1) + A__AND(2, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(1 + (1 + z039), 1 + z1), 1 + z039, z1) + A__AND(a__isNatIListKind(z039), 1 + z1) + A__ISNATKIND(1 + z039) :|: z1 >= 0, z039 >= 0, z = 1 + (1 + z039) + z1
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(1 + (1 + z040), 1 + z1), 1 + z040, z1) + A__AND(a__isNatKind(z040), 1 + z1) + A__ISNATKIND(1 + z040) :|: z1 >= 0, z040 >= 0, z = 1 + (1 + z040) + z1
   A__LENGTH(z) -{ 1 }-> 1 + A__U61(a__and(a__and(a__isNatList(z1), 1 + z1), 1 + (1 + z0) + (1 + z0)), z1) + A__AND(a__and(a__isNatList(z1), 1 + z1), 1 + (1 + z0) + (1 + z0)) + A__AND(a__isNatList(z1), 1 + z1) + A__ISNATLIST(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__U11(z, z') -{ 1 }-> 1 + A__ISNATLIST(z0) :|: z = 2, z0 >= 0, z' = z0
   A__U21(z, z') -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 2, z0 >= 0, z' = z0
   A__U31(z, z') -{ 1 }-> 1 + A__ISNATLIST(z0) :|: z = 2, z0 >= 0, z' = z0
   A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(a__U21(a__isNatKind(z0''), z0''), z1) + A__ISNAT(1 + z0'') :|: z = 2, z1 >= 0, z' = 1 + z0'', z0'' >= 0, z'' = z1
   A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(a__U11(a__isNatIListKind(z0'), z0'), z1) + A__ISNAT(1 + z0') :|: z = 2, z1 >= 0, z0' >= 0, z' = 1 + z0', z'' = z1
   A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(2, z1) + A__ISNAT(0) :|: z = 2, z1 >= 0, z' = 0, z'' = z1
   A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(0, z1) + A__ISNAT(z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1
   A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(1 + z0, z1) + A__ISNAT(z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1
   A__U42(z, z') -{ 1 }-> 1 + A__ISNATILIST(z0) :|: z = 2, z0 >= 0, z' = z0
   A__U51(z, z', z'') -{ 1 }-> 1 + A__U52(a__U21(a__isNatKind(z02), z02), z1) + A__ISNAT(1 + z02) :|: z = 2, z1 >= 0, z02 >= 0, z' = 1 + z02, z'' = z1
   A__U51(z, z', z'') -{ 1 }-> 1 + A__U52(a__U11(a__isNatIListKind(z01), z01), z1) + A__ISNAT(1 + z01) :|: z = 2, z1 >= 0, z01 >= 0, z' = 1 + z01, z'' = z1
   A__U51(z, z', z'') -{ 1 }-> 1 + A__U52(2, z1) + A__ISNAT(0) :|: z = 2, z1 >= 0, z' = 0, z'' = z1
   A__U51(z, z', z'') -{ 1 }-> 1 + A__U52(0, z1) + A__ISNAT(z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1
   A__U51(z, z', z'') -{ 1 }-> 1 + A__U52(1 + z0, z1) + A__ISNAT(z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1
   A__U52(z, z') -{ 1 }-> 1 + A__ISNATLIST(z0) :|: z = 2, z0 >= 0, z' = z0
   A__U61(z, z') -{ 1 }-> 1 + A__LENGTH(mark(z0)) + MARK(z0) :|: z = 2, z0 >= 0, z' = z0
   MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0
   MARK(z) -{ 1 }-> 1 + A__ISNATLIST(z0) :|: z = 1 + z0, z0 >= 0
   MARK(z) -{ 1 }-> 1 + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0
   MARK(z) -{ 1 }-> 1 + A__ISNATILISTKIND(z0) :|: z = 1 + z0, z0 >= 0
   MARK(z) -{ 1 }-> 1 + A__ISNATILIST(z0) :|: z = 1 + z0, z0 >= 0
   MARK(z) -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1 + z0, z0 >= 0
   MARK(z) -{ 1 }-> 1 + A__U61(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__U52(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__U51(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U42(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__U41(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U31(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__U21(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__U11(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__LENGTH(mark(z0)) + MARK(z0) :|: z = 1 + z0, z0 >= 0
   MARK(z) -{ 1 }-> 1 + A__AND(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__U11(z, z') -{ 0 }-> a__U12(a__U51(a__and(a__isNatKind(z0270), 1 + z1118), z0270, z1118)) :|: z = 2, z' = 1 + z0270 + z1118, z0270 >= 0, z1118 >= 0
   a__U11(z, z') -{ 0 }-> a__U12(2) :|: z = 2, z' = 1
   a__U11(z, z') -{ 0 }-> a__U12(0) :|: z = 2, z0 >= 0, z' = z0
   a__U11(z, z') -{ 0 }-> a__U12(1 + z0) :|: z = 2, z0 >= 0, z' = z0
   a__U11(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   a__U11(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   a__U12(z) -{ 0 }-> 2 :|: z = 2
   a__U12(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__U12(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__U21(z, z') -{ 0 }-> a__U22(a__U21(a__isNatKind(z0272), z0272)) :|: z = 2, z0272 >= 0, z' = 1 + z0272
   a__U21(z, z') -{ 0 }-> a__U22(a__U11(a__isNatIListKind(z0271), z0271)) :|: z = 2, z0271 >= 0, z' = 1 + z0271
   a__U21(z, z') -{ 0 }-> a__U22(2) :|: z = 2, z' = 0
   a__U21(z, z') -{ 0 }-> a__U22(0) :|: z = 2, z0 >= 0, z' = z0
   a__U21(z, z') -{ 0 }-> a__U22(1 + z0) :|: z = 2, z0 >= 0, z' = z0
   a__U21(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   a__U21(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   a__U22(z) -{ 0 }-> 2 :|: z = 2
   a__U22(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__U22(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__U31(z, z') -{ 0 }-> a__U32(a__U51(a__and(a__isNatKind(z0273), 1 + z1119), z0273, z1119)) :|: z = 2, z0273 >= 0, z' = 1 + z0273 + z1119, z1119 >= 0
   a__U31(z, z') -{ 0 }-> a__U32(2) :|: z = 2, z' = 1
   a__U31(z, z') -{ 0 }-> a__U32(0) :|: z = 2, z0 >= 0, z' = z0
   a__U31(z, z') -{ 0 }-> a__U32(1 + z0) :|: z = 2, z0 >= 0, z' = z0
   a__U31(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   a__U31(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   a__U32(z) -{ 0 }-> 2 :|: z = 2
   a__U32(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__U32(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__U41(z, z', z'') -{ 0 }-> a__U42(a__U21(a__isNatKind(z0275), z0275), z1) :|: z = 2, z' = 1 + z0275, z1 >= 0, z0275 >= 0, z'' = z1
   a__U41(z, z', z'') -{ 0 }-> a__U42(a__U11(a__isNatIListKind(z0274), z0274), z1) :|: z = 2, z1 >= 0, z' = 1 + z0274, z'' = z1, z0274 >= 0
   a__U41(z, z', z'') -{ 0 }-> a__U42(2, z1) :|: z = 2, z1 >= 0, z' = 0, z'' = z1
   a__U41(z, z', z'') -{ 0 }-> a__U42(0, z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1
   a__U41(z, z', z'') -{ 0 }-> a__U42(1 + z0, z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1
   a__U41(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   a__U41(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0
   a__U42(z, z') -{ 0 }-> a__U43(a__U41(a__and(a__isNatKind(z0276), 1 + z1120), z0276, z1120)) :|: z = 2, z0276 >= 0, z' = 1 + z0276 + z1120, z1120 >= 0
   a__U42(z, z') -{ 0 }-> a__U43(a__U31(a__isNatIListKind(z0), z0)) :|: z = 2, z0 >= 0, z' = z0
   a__U42(z, z') -{ 0 }-> a__U43(2) :|: z = 2, z' = 3
   a__U42(z, z') -{ 0 }-> a__U43(0) :|: z = 2, z0 >= 0, z' = z0
   a__U42(z, z') -{ 0 }-> a__U43(1 + z0) :|: z = 2, z0 >= 0, z' = z0
   a__U42(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   a__U42(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   a__U43(z) -{ 0 }-> 2 :|: z = 2
   a__U43(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__U43(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__U51(z, z', z'') -{ 0 }-> a__U52(a__U21(a__isNatKind(z0278), z0278), z1) :|: z = 2, z' = 1 + z0278, z1 >= 0, z0278 >= 0, z'' = z1
   a__U51(z, z', z'') -{ 0 }-> a__U52(a__U11(a__isNatIListKind(z0277), z0277), z1) :|: z = 2, z0277 >= 0, z1 >= 0, z' = 1 + z0277, z'' = z1
   a__U51(z, z', z'') -{ 0 }-> a__U52(2, z1) :|: z = 2, z1 >= 0, z' = 0, z'' = z1
   a__U51(z, z', z'') -{ 0 }-> a__U52(0, z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1
   a__U51(z, z', z'') -{ 0 }-> a__U52(1 + z0, z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1
   a__U51(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   a__U51(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0
   a__U52(z, z') -{ 0 }-> a__U53(a__U51(a__and(a__isNatKind(z0279), 1 + z1121), z0279, z1121)) :|: z = 2, z0279 >= 0, z' = 1 + z0279 + z1121, z1121 >= 0
   a__U52(z, z') -{ 0 }-> a__U53(2) :|: z = 2, z' = 1
   a__U52(z, z') -{ 0 }-> a__U53(0) :|: z = 2, z0 >= 0, z' = z0
   a__U52(z, z') -{ 0 }-> a__U53(1 + z0) :|: z = 2, z0 >= 0, z' = z0
   a__U52(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   a__U52(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   a__U53(z) -{ 0 }-> 2 :|: z = 2
   a__U53(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__U53(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__U61(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   a__U61(z, z') -{ 0 }-> 1 + a__length(mark(z0)) :|: z = 2, z0 >= 0, z' = z0
   a__U61(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   a__and(z, z') -{ 0 }-> mark(z0) :|: z = 2, z0 >= 0, z' = z0
   a__and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   a__and(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   a__isNat(z) -{ 0 }-> a__U21(a__isNatKind(z0304), 1 + z0304) :|: z = 1 + (1 + z0304), z0304 >= 0
   a__isNat(z) -{ 0 }-> a__U21(a__isNatIListKind(z0303), 1 + z0303) :|: z = 1 + (1 + z0303), z0303 >= 0
   a__isNat(z) -{ 0 }-> a__U21(2, 0) :|: z = 1 + 0
   a__isNat(z) -{ 0 }-> a__U21(0, z0) :|: z = 1 + z0, z0 >= 0
   a__isNat(z) -{ 0 }-> a__U21(1 + z0, z0) :|: z = 1 + z0, z0 >= 0
   a__isNat(z) -{ 0 }-> a__U11(a__and(a__isNatKind(z0302), 1 + z1132), 1 + z0302 + z1132) :|: z0302 >= 0, z = 1 + (1 + z0302 + z1132), z1132 >= 0
   a__isNat(z) -{ 0 }-> a__U11(2, 3) :|: z = 1 + 3
   a__isNat(z) -{ 0 }-> a__U11(2, 1) :|: z = 1 + 1
   a__isNat(z) -{ 0 }-> a__U11(0, z0) :|: z = 1 + z0, z0 >= 0
   a__isNat(z) -{ 0 }-> a__U11(1 + z0, z0) :|: z = 1 + z0, z0 >= 0
   a__isNat(z) -{ 0 }-> 2 :|: z = 0
   a__isNat(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__isNat(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__isNatIList(z) -{ 0 }-> a__U41(a__and(a__isNatKind(z0307), 1 + z1), 1 + z0307, z1) :|: z1 >= 0, z0307 >= 0, z = 1 + (1 + z0307) + z1
   a__isNatIList(z) -{ 0 }-> a__U41(a__and(a__isNatIListKind(z0306), 1 + z1), 1 + z0306, z1) :|: z0306 >= 0, z1 >= 0, z = 1 + (1 + z0306) + z1
   a__isNatIList(z) -{ 0 }-> a__U41(a__and(2, 1 + z1), 0, z1) :|: z1 >= 0, z = 1 + 0 + z1
   a__isNatIList(z) -{ 0 }-> a__U41(a__and(0, 1 + z1), z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__isNatIList(z) -{ 0 }-> a__U41(a__and(1 + z0, 1 + z1), z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__isNatIList(z) -{ 0 }-> a__U31(a__and(a__isNatKind(z0305), 1 + z1133), 1 + z0305 + z1133) :|: z = 1 + z0305 + z1133, z1133 >= 0, z0305 >= 0
   a__isNatIList(z) -{ 0 }-> a__U31(2, 3) :|: z = 3
   a__isNatIList(z) -{ 0 }-> a__U31(2, 1) :|: z = 1
   a__isNatIList(z) -{ 0 }-> a__U31(0, z0) :|: z = z0, z0 >= 0
   a__isNatIList(z) -{ 0 }-> a__U31(1 + z0, z0) :|: z = z0, z0 >= 0
   a__isNatIList(z) -{ 0 }-> 2 :|: z = 3
   a__isNatIList(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__isNatIList(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__isNatIListKind(z) -{ 0 }-> a__and(a__isNatKind(z0309), 1 + z1) :|: z1 >= 0, z = 1 + (1 + z0309) + z1, z0309 >= 0
   a__isNatIListKind(z) -{ 0 }-> a__and(a__isNatIListKind(z0308), 1 + z1) :|: z1 >= 0, z0308 >= 0, z = 1 + (1 + z0308) + z1
   a__isNatIListKind(z) -{ 0 }-> a__and(2, 1 + z1) :|: z1 >= 0, z = 1 + 0 + z1
   a__isNatIListKind(z) -{ 0 }-> a__and(0, 1 + z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__isNatIListKind(z) -{ 0 }-> a__and(1 + z0, 1 + z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__isNatIListKind(z) -{ 0 }-> 2 :|: z = 1
   a__isNatIListKind(z) -{ 0 }-> 2 :|: z = 3
   a__isNatIListKind(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__isNatIListKind(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__isNatKind(z) -{ 0 }-> a__isNatKind(z0) :|: z = 1 + z0, z0 >= 0
   a__isNatKind(z) -{ 0 }-> a__isNatIListKind(z0) :|: z = 1 + z0, z0 >= 0
   a__isNatKind(z) -{ 0 }-> 2 :|: z = 0
   a__isNatKind(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__isNatKind(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__isNatList(z) -{ 0 }-> a__U51(a__and(a__isNatKind(z0311), 1 + z1), 1 + z0311, z1) :|: z1 >= 0, z = 1 + (1 + z0311) + z1, z0311 >= 0
   a__isNatList(z) -{ 0 }-> a__U51(a__and(a__isNatIListKind(z0310), 1 + z1), 1 + z0310, z1) :|: z1 >= 0, z0310 >= 0, z = 1 + (1 + z0310) + z1
   a__isNatList(z) -{ 0 }-> a__U51(a__and(2, 1 + z1), 0, z1) :|: z1 >= 0, z = 1 + 0 + z1
   a__isNatList(z) -{ 0 }-> a__U51(a__and(0, 1 + z1), z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__isNatList(z) -{ 0 }-> a__U51(a__and(1 + z0, 1 + z1), z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__isNatList(z) -{ 0 }-> 2 :|: z = 1
   a__isNatList(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__isNatList(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__length(z) -{ 0 }-> a__U61(a__and(a__and(a__U51(a__and(a__isNatKind(z0312), 1 + z1134), z0312, z1134), 1 + (1 + z0312 + z1134)), 1 + (1 + z0) + (1 + z0)), 1 + z0312 + z1134) :|: z1134 >= 0, z = 1 + z0 + (1 + z0312 + z1134), z0 >= 0, z0312 >= 0
   a__length(z) -{ 0 }-> a__U61(a__and(a__and(2, 1 + 1), 1 + (1 + z0) + (1 + z0)), 1) :|: z0 >= 0, z = 1 + z0 + 1
   a__length(z) -{ 0 }-> a__U61(a__and(a__and(0, 1 + z1), 1 + (1 + z0) + (1 + z0)), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__length(z) -{ 0 }-> a__U61(a__and(a__and(1 + z1, 1 + z1), 1 + (1 + z0) + (1 + z0)), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__length(z) -{ 0 }-> 0 :|: z = 1
   a__length(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__length(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__zeros -{ 0 }-> 3 :|: 
   a__zeros -{ 0 }-> 0 :|: 
   a__zeros -{ 0 }-> 1 + 0 + 3 :|: 
   mark(z) -{ 0 }-> a__zeros :|: z = 3
   mark(z) -{ 0 }-> a__length(mark(z0)) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__isNatList(z0) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__isNatKind(z0) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__isNatIListKind(z0) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__isNatIList(z0) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__isNat(z0) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__and(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__U61(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__U53(mark(z0)) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__U52(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__U51(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U43(mark(z0)) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__U42(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__U41(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U32(mark(z0)) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__U31(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__U22(mark(z0)) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__U21(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__U12(mark(z0)) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__U11(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> 2 :|: z = 2
   mark(z) -{ 0 }-> 1 :|: z = 1
   mark(z) -{ 0 }-> 0 :|: z = 0
   mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   mark(z) -{ 0 }-> 1 + mark(z0) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> 1 + mark(z0) + z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1


----------------------------------------

(37) InliningProof (UPPER BOUND(ID))
Inlined the following terminating rules on right-hand sides where appropriate:

   a__zeros -{ 0 }-> 3 :|: 
   a__zeros -{ 0 }-> 0 :|: 
   a__zeros -{ 0 }-> 1 + 0 + 3 :|: 
   a__U12(z) -{ 0 }-> 2 :|: z = 2
   a__U12(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__U12(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__U22(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__U22(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__U22(z) -{ 0 }-> 2 :|: z = 2
   a__U32(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__U32(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__U32(z) -{ 0 }-> 2 :|: z = 2
   a__U43(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__U43(z) -{ 0 }-> 2 :|: z = 2
   a__U43(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__U53(z) -{ 0 }-> 2 :|: z = 2
   a__U53(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__U53(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0

----------------------------------------

(38)
Obligation:
Complexity RNTS consisting of the following rules:

   A__AND(z, z') -{ 1 }-> 1 + MARK(z0) :|: z = 2, z0 >= 0, z' = z0
   A__ISNAT(z) -{ 1 }-> 1 + A__U21(a__isNatKind(z027), 1 + z027) + A__ISNATKIND(1 + z027) :|: z027 >= 0, z = 1 + (1 + z027)
   A__ISNAT(z) -{ 1 }-> 1 + A__U21(a__isNatIListKind(z026), 1 + z026) + A__ISNATKIND(1 + z026) :|: z = 1 + (1 + z026), z026 >= 0
   A__ISNAT(z) -{ 1 }-> 1 + A__U21(2, 0) + A__ISNATKIND(0) :|: z = 1 + 0
   A__ISNAT(z) -{ 1 }-> 1 + A__U21(0, z0) + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0
   A__ISNAT(z) -{ 1 }-> 1 + A__U21(1 + z0, z0) + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0
   A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(a__isNatKind(z025), 1 + z19), 1 + z025 + z19) + A__ISNATILISTKIND(1 + z025 + z19) :|: z025 >= 0, z = 1 + (1 + z025 + z19), z19 >= 0
   A__ISNAT(z) -{ 1 }-> 1 + A__U11(2, 3) + A__ISNATILISTKIND(3) :|: z = 1 + 3
   A__ISNAT(z) -{ 1 }-> 1 + A__U11(2, 1) + A__ISNATILISTKIND(1) :|: z = 1 + 1
   A__ISNAT(z) -{ 1 }-> 1 + A__U11(0, z0) + A__ISNATILISTKIND(z0) :|: z = 1 + z0, z0 >= 0
   A__ISNAT(z) -{ 1 }-> 1 + A__U11(1 + z0, z0) + A__ISNATILISTKIND(z0) :|: z = 1 + z0, z0 >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U31(a__and(a__isNatKind(z028), 1 + z110), 1 + z028 + z110) + A__ISNATILISTKIND(1 + z028 + z110) :|: z110 >= 0, z = 1 + z028 + z110, z028 >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U31(2, 3) + A__ISNATILISTKIND(3) :|: z = 3
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U31(2, 1) + A__ISNATILISTKIND(1) :|: z = 1
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U31(0, z0) + A__ISNATILISTKIND(z0) :|: z = z0, z0 >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U31(1 + z0, z0) + A__ISNATILISTKIND(z0) :|: z = z0, z0 >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(a__isNatKind(z030), 1 + z1), 1 + z030, z1) + A__AND(a__isNatKind(z030), 1 + z1) + A__ISNATKIND(1 + z030) :|: z1 >= 0, z = 1 + (1 + z030) + z1, z030 >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(a__isNatKind(z030), 1 + z1), 1 + z030, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(1 + z030) :|: z1 >= 0, z = 1 + (1 + z030) + z1, z030 >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(a__isNatKind(z030), 1 + z1), 1 + z030, z1) + A__AND(1 + (1 + z030), 1 + z1) + A__ISNATKIND(1 + z030) :|: z1 >= 0, z = 1 + (1 + z030) + z1, z030 >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(a__isNatIListKind(z029), 1 + z1), 1 + z029, z1) + A__AND(a__isNatIListKind(z029), 1 + z1) + A__ISNATKIND(1 + z029) :|: z029 >= 0, z = 1 + (1 + z029) + z1, z1 >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(a__isNatIListKind(z029), 1 + z1), 1 + z029, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(1 + z029) :|: z029 >= 0, z = 1 + (1 + z029) + z1, z1 >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(a__isNatIListKind(z029), 1 + z1), 1 + z029, z1) + A__AND(1 + (1 + z029), 1 + z1) + A__ISNATKIND(1 + z029) :|: z029 >= 0, z = 1 + (1 + z029) + z1, z1 >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(2, 1 + z1), 0, z1) + A__AND(2, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(2, 1 + z1), 0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(2, 1 + z1), 0, z1) + A__AND(1 + 0, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(0, 1 + z1), z0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(0, 1 + z1), z0, z1) + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(0, 1 + z1), 0, z1) + A__AND(2, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(0, 1 + z1), 1 + z033, z1) + A__AND(a__isNatIListKind(z033), 1 + z1) + A__ISNATKIND(1 + z033) :|: z1 >= 0, z = 1 + (1 + z033) + z1, z033 >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(0, 1 + z1), 1 + z034, z1) + A__AND(a__isNatKind(z034), 1 + z1) + A__ISNATKIND(1 + z034) :|: z1 >= 0, z034 >= 0, z = 1 + (1 + z034) + z1
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(1 + z0, 1 + z1), z0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(1 + z0, 1 + z1), z0, z1) + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(1 + 0, 1 + z1), 0, z1) + A__AND(2, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(1 + (1 + z031), 1 + z1), 1 + z031, z1) + A__AND(a__isNatIListKind(z031), 1 + z1) + A__ISNATKIND(1 + z031) :|: z = 1 + (1 + z031) + z1, z031 >= 0, z1 >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(1 + (1 + z032), 1 + z1), 1 + z032, z1) + A__AND(a__isNatKind(z032), 1 + z1) + A__ISNATKIND(1 + z032) :|: z032 >= 0, z1 >= 0, z = 1 + (1 + z032) + z1
   A__ISNATILISTKIND(z) -{ 1 }-> 1 + A__AND(a__isNatKind(z036), 1 + z1) + A__ISNATKIND(1 + z036) :|: z036 >= 0, z1 >= 0, z = 1 + (1 + z036) + z1
   A__ISNATILISTKIND(z) -{ 1 }-> 1 + A__AND(a__isNatIListKind(z035), 1 + z1) + A__ISNATKIND(1 + z035) :|: z035 >= 0, z1 >= 0, z = 1 + (1 + z035) + z1
   A__ISNATILISTKIND(z) -{ 1 }-> 1 + A__AND(2, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1
   A__ISNATILISTKIND(z) -{ 1 }-> 1 + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__ISNATILISTKIND(z) -{ 1 }-> 1 + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__ISNATKIND(z) -{ 1 }-> 1 + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0
   A__ISNATKIND(z) -{ 1 }-> 1 + A__ISNATILISTKIND(z0) :|: z = 1 + z0, z0 >= 0
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(a__isNatKind(z038), 1 + z1), 1 + z038, z1) + A__AND(a__isNatKind(z038), 1 + z1) + A__ISNATKIND(1 + z038) :|: z1 >= 0, z = 1 + (1 + z038) + z1, z038 >= 0
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(a__isNatKind(z038), 1 + z1), 1 + z038, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(1 + z038) :|: z1 >= 0, z = 1 + (1 + z038) + z1, z038 >= 0
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(a__isNatKind(z038), 1 + z1), 1 + z038, z1) + A__AND(1 + (1 + z038), 1 + z1) + A__ISNATKIND(1 + z038) :|: z1 >= 0, z = 1 + (1 + z038) + z1, z038 >= 0
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(a__isNatIListKind(z037), 1 + z1), 1 + z037, z1) + A__AND(a__isNatIListKind(z037), 1 + z1) + A__ISNATKIND(1 + z037) :|: z1 >= 0, z = 1 + (1 + z037) + z1, z037 >= 0
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(a__isNatIListKind(z037), 1 + z1), 1 + z037, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(1 + z037) :|: z1 >= 0, z = 1 + (1 + z037) + z1, z037 >= 0
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(a__isNatIListKind(z037), 1 + z1), 1 + z037, z1) + A__AND(1 + (1 + z037), 1 + z1) + A__ISNATKIND(1 + z037) :|: z1 >= 0, z = 1 + (1 + z037) + z1, z037 >= 0
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(2, 1 + z1), 0, z1) + A__AND(2, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(2, 1 + z1), 0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(2, 1 + z1), 0, z1) + A__AND(1 + 0, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(0, 1 + z1), z0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(0, 1 + z1), z0, z1) + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(0, 1 + z1), 0, z1) + A__AND(2, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(0, 1 + z1), 1 + z041, z1) + A__AND(a__isNatIListKind(z041), 1 + z1) + A__ISNATKIND(1 + z041) :|: z1 >= 0, z041 >= 0, z = 1 + (1 + z041) + z1
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(0, 1 + z1), 1 + z042, z1) + A__AND(a__isNatKind(z042), 1 + z1) + A__ISNATKIND(1 + z042) :|: z042 >= 0, z1 >= 0, z = 1 + (1 + z042) + z1
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(1 + z0, 1 + z1), z0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(1 + z0, 1 + z1), z0, z1) + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(1 + 0, 1 + z1), 0, z1) + A__AND(2, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(1 + (1 + z039), 1 + z1), 1 + z039, z1) + A__AND(a__isNatIListKind(z039), 1 + z1) + A__ISNATKIND(1 + z039) :|: z1 >= 0, z039 >= 0, z = 1 + (1 + z039) + z1
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(1 + (1 + z040), 1 + z1), 1 + z040, z1) + A__AND(a__isNatKind(z040), 1 + z1) + A__ISNATKIND(1 + z040) :|: z1 >= 0, z040 >= 0, z = 1 + (1 + z040) + z1
   A__LENGTH(z) -{ 1 }-> 1 + A__U61(a__and(a__and(a__isNatList(z1), 1 + z1), 1 + (1 + z0) + (1 + z0)), z1) + A__AND(a__and(a__isNatList(z1), 1 + z1), 1 + (1 + z0) + (1 + z0)) + A__AND(a__isNatList(z1), 1 + z1) + A__ISNATLIST(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__U11(z, z') -{ 1 }-> 1 + A__ISNATLIST(z0) :|: z = 2, z0 >= 0, z' = z0
   A__U21(z, z') -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 2, z0 >= 0, z' = z0
   A__U31(z, z') -{ 1 }-> 1 + A__ISNATLIST(z0) :|: z = 2, z0 >= 0, z' = z0
   A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(a__U21(a__isNatKind(z0''), z0''), z1) + A__ISNAT(1 + z0'') :|: z = 2, z1 >= 0, z' = 1 + z0'', z0'' >= 0, z'' = z1
   A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(a__U11(a__isNatIListKind(z0'), z0'), z1) + A__ISNAT(1 + z0') :|: z = 2, z1 >= 0, z0' >= 0, z' = 1 + z0', z'' = z1
   A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(2, z1) + A__ISNAT(0) :|: z = 2, z1 >= 0, z' = 0, z'' = z1
   A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(0, z1) + A__ISNAT(z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1
   A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(1 + z0, z1) + A__ISNAT(z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1
   A__U42(z, z') -{ 1 }-> 1 + A__ISNATILIST(z0) :|: z = 2, z0 >= 0, z' = z0
   A__U51(z, z', z'') -{ 1 }-> 1 + A__U52(a__U21(a__isNatKind(z02), z02), z1) + A__ISNAT(1 + z02) :|: z = 2, z1 >= 0, z02 >= 0, z' = 1 + z02, z'' = z1
   A__U51(z, z', z'') -{ 1 }-> 1 + A__U52(a__U11(a__isNatIListKind(z01), z01), z1) + A__ISNAT(1 + z01) :|: z = 2, z1 >= 0, z01 >= 0, z' = 1 + z01, z'' = z1
   A__U51(z, z', z'') -{ 1 }-> 1 + A__U52(2, z1) + A__ISNAT(0) :|: z = 2, z1 >= 0, z' = 0, z'' = z1
   A__U51(z, z', z'') -{ 1 }-> 1 + A__U52(0, z1) + A__ISNAT(z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1
   A__U51(z, z', z'') -{ 1 }-> 1 + A__U52(1 + z0, z1) + A__ISNAT(z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1
   A__U52(z, z') -{ 1 }-> 1 + A__ISNATLIST(z0) :|: z = 2, z0 >= 0, z' = z0
   A__U61(z, z') -{ 1 }-> 1 + A__LENGTH(mark(z0)) + MARK(z0) :|: z = 2, z0 >= 0, z' = z0
   MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0
   MARK(z) -{ 1 }-> 1 + A__ISNATLIST(z0) :|: z = 1 + z0, z0 >= 0
   MARK(z) -{ 1 }-> 1 + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0
   MARK(z) -{ 1 }-> 1 + A__ISNATILISTKIND(z0) :|: z = 1 + z0, z0 >= 0
   MARK(z) -{ 1 }-> 1 + A__ISNATILIST(z0) :|: z = 1 + z0, z0 >= 0
   MARK(z) -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1 + z0, z0 >= 0
   MARK(z) -{ 1 }-> 1 + A__U61(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__U52(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__U51(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U42(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__U41(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U31(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__U21(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__U11(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__LENGTH(mark(z0)) + MARK(z0) :|: z = 1 + z0, z0 >= 0
   MARK(z) -{ 1 }-> 1 + A__AND(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__U11(z, z') -{ 0 }-> a__U12(a__U51(a__and(a__isNatKind(z0270), 1 + z1118), z0270, z1118)) :|: z = 2, z' = 1 + z0270 + z1118, z0270 >= 0, z1118 >= 0
   a__U11(z, z') -{ 0 }-> 2 :|: z = 2, z' = 1, 2 = 2
   a__U11(z, z') -{ 0 }-> 2 :|: z = 2, z0 >= 0, z' = z0, 1 + z0 = 2
   a__U11(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   a__U11(z, z') -{ 0 }-> 0 :|: z = 2, z' = 1, v0 >= 0, 2 = v0
   a__U11(z, z') -{ 0 }-> 0 :|: z = 2, z0 >= 0, z' = z0, v0 >= 0, 1 + z0 = v0
   a__U11(z, z') -{ 0 }-> 0 :|: z = 2, z0 >= 0, z' = z0, v0 >= 0, 0 = v0
   a__U11(z, z') -{ 0 }-> 1 + z0 :|: z = 2, z' = 1, 2 = z0, z0 >= 0
   a__U11(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z0 >= 0, z' = z0, 1 + z0 = z0', z0' >= 0
   a__U11(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z0 >= 0, z' = z0, 0 = z0', z0' >= 0
   a__U11(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   a__U12(z) -{ 0 }-> 2 :|: z = 2
   a__U12(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__U12(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__U21(z, z') -{ 0 }-> a__U22(a__U21(a__isNatKind(z0272), z0272)) :|: z = 2, z0272 >= 0, z' = 1 + z0272
   a__U21(z, z') -{ 0 }-> a__U22(a__U11(a__isNatIListKind(z0271), z0271)) :|: z = 2, z0271 >= 0, z' = 1 + z0271
   a__U21(z, z') -{ 0 }-> 2 :|: z = 2, z' = 0, 2 = 2
   a__U21(z, z') -{ 0 }-> 2 :|: z = 2, z0 >= 0, z' = z0, 1 + z0 = 2
   a__U21(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   a__U21(z, z') -{ 0 }-> 0 :|: z = 2, z' = 0, v0 >= 0, 2 = v0
   a__U21(z, z') -{ 0 }-> 0 :|: z = 2, z0 >= 0, z' = z0, v0 >= 0, 1 + z0 = v0
   a__U21(z, z') -{ 0 }-> 0 :|: z = 2, z0 >= 0, z' = z0, v0 >= 0, 0 = v0
   a__U21(z, z') -{ 0 }-> 1 + z0 :|: z = 2, z' = 0, 2 = z0, z0 >= 0
   a__U21(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z0 >= 0, z' = z0, 1 + z0 = z0', z0' >= 0
   a__U21(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z0 >= 0, z' = z0, 0 = z0', z0' >= 0
   a__U21(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   a__U22(z) -{ 0 }-> 2 :|: z = 2
   a__U22(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__U22(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__U31(z, z') -{ 0 }-> a__U32(a__U51(a__and(a__isNatKind(z0273), 1 + z1119), z0273, z1119)) :|: z = 2, z0273 >= 0, z' = 1 + z0273 + z1119, z1119 >= 0
   a__U31(z, z') -{ 0 }-> 2 :|: z = 2, z' = 1, 2 = 2
   a__U31(z, z') -{ 0 }-> 2 :|: z = 2, z0 >= 0, z' = z0, 1 + z0 = 2
   a__U31(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   a__U31(z, z') -{ 0 }-> 0 :|: z = 2, z' = 1, v0 >= 0, 2 = v0
   a__U31(z, z') -{ 0 }-> 0 :|: z = 2, z0 >= 0, z' = z0, v0 >= 0, 1 + z0 = v0
   a__U31(z, z') -{ 0 }-> 0 :|: z = 2, z0 >= 0, z' = z0, v0 >= 0, 0 = v0
   a__U31(z, z') -{ 0 }-> 1 + z0 :|: z = 2, z' = 1, 2 = z0, z0 >= 0
   a__U31(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z0 >= 0, z' = z0, 1 + z0 = z0', z0' >= 0
   a__U31(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z0 >= 0, z' = z0, 0 = z0', z0' >= 0
   a__U31(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   a__U32(z) -{ 0 }-> 2 :|: z = 2
   a__U32(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__U32(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__U41(z, z', z'') -{ 0 }-> a__U42(a__U21(a__isNatKind(z0275), z0275), z1) :|: z = 2, z' = 1 + z0275, z1 >= 0, z0275 >= 0, z'' = z1
   a__U41(z, z', z'') -{ 0 }-> a__U42(a__U11(a__isNatIListKind(z0274), z0274), z1) :|: z = 2, z1 >= 0, z' = 1 + z0274, z'' = z1, z0274 >= 0
   a__U41(z, z', z'') -{ 0 }-> a__U42(2, z1) :|: z = 2, z1 >= 0, z' = 0, z'' = z1
   a__U41(z, z', z'') -{ 0 }-> a__U42(0, z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1
   a__U41(z, z', z'') -{ 0 }-> a__U42(1 + z0, z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1
   a__U41(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   a__U41(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0
   a__U42(z, z') -{ 0 }-> a__U43(a__U41(a__and(a__isNatKind(z0276), 1 + z1120), z0276, z1120)) :|: z = 2, z0276 >= 0, z' = 1 + z0276 + z1120, z1120 >= 0
   a__U42(z, z') -{ 0 }-> a__U43(a__U31(a__isNatIListKind(z0), z0)) :|: z = 2, z0 >= 0, z' = z0
   a__U42(z, z') -{ 0 }-> 2 :|: z = 2, z' = 3, 2 = 2
   a__U42(z, z') -{ 0 }-> 2 :|: z = 2, z0 >= 0, z' = z0, 1 + z0 = 2
   a__U42(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   a__U42(z, z') -{ 0 }-> 0 :|: z = 2, z' = 3, v0 >= 0, 2 = v0
   a__U42(z, z') -{ 0 }-> 0 :|: z = 2, z0 >= 0, z' = z0, v0 >= 0, 1 + z0 = v0
   a__U42(z, z') -{ 0 }-> 0 :|: z = 2, z0 >= 0, z' = z0, v0 >= 0, 0 = v0
   a__U42(z, z') -{ 0 }-> 1 + z0 :|: z = 2, z' = 3, 2 = z0, z0 >= 0
   a__U42(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z0 >= 0, z' = z0, 1 + z0 = z0', z0' >= 0
   a__U42(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z0 >= 0, z' = z0, 0 = z0', z0' >= 0
   a__U42(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   a__U43(z) -{ 0 }-> 2 :|: z = 2
   a__U43(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__U43(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__U51(z, z', z'') -{ 0 }-> a__U52(a__U21(a__isNatKind(z0278), z0278), z1) :|: z = 2, z' = 1 + z0278, z1 >= 0, z0278 >= 0, z'' = z1
   a__U51(z, z', z'') -{ 0 }-> a__U52(a__U11(a__isNatIListKind(z0277), z0277), z1) :|: z = 2, z0277 >= 0, z1 >= 0, z' = 1 + z0277, z'' = z1
   a__U51(z, z', z'') -{ 0 }-> a__U52(2, z1) :|: z = 2, z1 >= 0, z' = 0, z'' = z1
   a__U51(z, z', z'') -{ 0 }-> a__U52(0, z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1
   a__U51(z, z', z'') -{ 0 }-> a__U52(1 + z0, z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1
   a__U51(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   a__U51(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0
   a__U52(z, z') -{ 0 }-> a__U53(a__U51(a__and(a__isNatKind(z0279), 1 + z1121), z0279, z1121)) :|: z = 2, z0279 >= 0, z' = 1 + z0279 + z1121, z1121 >= 0
   a__U52(z, z') -{ 0 }-> 2 :|: z = 2, z' = 1, 2 = 2
   a__U52(z, z') -{ 0 }-> 2 :|: z = 2, z0 >= 0, z' = z0, 1 + z0 = 2
   a__U52(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   a__U52(z, z') -{ 0 }-> 0 :|: z = 2, z' = 1, v0 >= 0, 2 = v0
   a__U52(z, z') -{ 0 }-> 0 :|: z = 2, z0 >= 0, z' = z0, v0 >= 0, 1 + z0 = v0
   a__U52(z, z') -{ 0 }-> 0 :|: z = 2, z0 >= 0, z' = z0, v0 >= 0, 0 = v0
   a__U52(z, z') -{ 0 }-> 1 + z0 :|: z = 2, z' = 1, 2 = z0, z0 >= 0
   a__U52(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z0 >= 0, z' = z0, 1 + z0 = z0', z0' >= 0
   a__U52(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z0 >= 0, z' = z0, 0 = z0', z0' >= 0
   a__U52(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   a__U53(z) -{ 0 }-> 2 :|: z = 2
   a__U53(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__U53(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__U61(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   a__U61(z, z') -{ 0 }-> 1 + a__length(mark(z0)) :|: z = 2, z0 >= 0, z' = z0
   a__U61(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   a__and(z, z') -{ 0 }-> mark(z0) :|: z = 2, z0 >= 0, z' = z0
   a__and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   a__and(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   a__isNat(z) -{ 0 }-> a__U21(a__isNatKind(z0304), 1 + z0304) :|: z = 1 + (1 + z0304), z0304 >= 0
   a__isNat(z) -{ 0 }-> a__U21(a__isNatIListKind(z0303), 1 + z0303) :|: z = 1 + (1 + z0303), z0303 >= 0
   a__isNat(z) -{ 0 }-> a__U21(2, 0) :|: z = 1 + 0
   a__isNat(z) -{ 0 }-> a__U21(0, z0) :|: z = 1 + z0, z0 >= 0
   a__isNat(z) -{ 0 }-> a__U21(1 + z0, z0) :|: z = 1 + z0, z0 >= 0
   a__isNat(z) -{ 0 }-> a__U11(a__and(a__isNatKind(z0302), 1 + z1132), 1 + z0302 + z1132) :|: z0302 >= 0, z = 1 + (1 + z0302 + z1132), z1132 >= 0
   a__isNat(z) -{ 0 }-> a__U11(2, 3) :|: z = 1 + 3
   a__isNat(z) -{ 0 }-> a__U11(2, 1) :|: z = 1 + 1
   a__isNat(z) -{ 0 }-> a__U11(0, z0) :|: z = 1 + z0, z0 >= 0
   a__isNat(z) -{ 0 }-> a__U11(1 + z0, z0) :|: z = 1 + z0, z0 >= 0
   a__isNat(z) -{ 0 }-> 2 :|: z = 0
   a__isNat(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__isNat(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__isNatIList(z) -{ 0 }-> a__U41(a__and(a__isNatKind(z0307), 1 + z1), 1 + z0307, z1) :|: z1 >= 0, z0307 >= 0, z = 1 + (1 + z0307) + z1
   a__isNatIList(z) -{ 0 }-> a__U41(a__and(a__isNatIListKind(z0306), 1 + z1), 1 + z0306, z1) :|: z0306 >= 0, z1 >= 0, z = 1 + (1 + z0306) + z1
   a__isNatIList(z) -{ 0 }-> a__U41(a__and(2, 1 + z1), 0, z1) :|: z1 >= 0, z = 1 + 0 + z1
   a__isNatIList(z) -{ 0 }-> a__U41(a__and(0, 1 + z1), z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__isNatIList(z) -{ 0 }-> a__U41(a__and(1 + z0, 1 + z1), z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__isNatIList(z) -{ 0 }-> a__U31(a__and(a__isNatKind(z0305), 1 + z1133), 1 + z0305 + z1133) :|: z = 1 + z0305 + z1133, z1133 >= 0, z0305 >= 0
   a__isNatIList(z) -{ 0 }-> a__U31(2, 3) :|: z = 3
   a__isNatIList(z) -{ 0 }-> a__U31(2, 1) :|: z = 1
   a__isNatIList(z) -{ 0 }-> a__U31(0, z0) :|: z = z0, z0 >= 0
   a__isNatIList(z) -{ 0 }-> a__U31(1 + z0, z0) :|: z = z0, z0 >= 0
   a__isNatIList(z) -{ 0 }-> 2 :|: z = 3
   a__isNatIList(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__isNatIList(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__isNatIListKind(z) -{ 0 }-> a__and(a__isNatKind(z0309), 1 + z1) :|: z1 >= 0, z = 1 + (1 + z0309) + z1, z0309 >= 0
   a__isNatIListKind(z) -{ 0 }-> a__and(a__isNatIListKind(z0308), 1 + z1) :|: z1 >= 0, z0308 >= 0, z = 1 + (1 + z0308) + z1
   a__isNatIListKind(z) -{ 0 }-> a__and(2, 1 + z1) :|: z1 >= 0, z = 1 + 0 + z1
   a__isNatIListKind(z) -{ 0 }-> a__and(0, 1 + z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__isNatIListKind(z) -{ 0 }-> a__and(1 + z0, 1 + z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__isNatIListKind(z) -{ 0 }-> 2 :|: z = 1
   a__isNatIListKind(z) -{ 0 }-> 2 :|: z = 3
   a__isNatIListKind(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__isNatIListKind(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__isNatKind(z) -{ 0 }-> a__isNatKind(z0) :|: z = 1 + z0, z0 >= 0
   a__isNatKind(z) -{ 0 }-> a__isNatIListKind(z0) :|: z = 1 + z0, z0 >= 0
   a__isNatKind(z) -{ 0 }-> 2 :|: z = 0
   a__isNatKind(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__isNatKind(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__isNatList(z) -{ 0 }-> a__U51(a__and(a__isNatKind(z0311), 1 + z1), 1 + z0311, z1) :|: z1 >= 0, z = 1 + (1 + z0311) + z1, z0311 >= 0
   a__isNatList(z) -{ 0 }-> a__U51(a__and(a__isNatIListKind(z0310), 1 + z1), 1 + z0310, z1) :|: z1 >= 0, z0310 >= 0, z = 1 + (1 + z0310) + z1
   a__isNatList(z) -{ 0 }-> a__U51(a__and(2, 1 + z1), 0, z1) :|: z1 >= 0, z = 1 + 0 + z1
   a__isNatList(z) -{ 0 }-> a__U51(a__and(0, 1 + z1), z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__isNatList(z) -{ 0 }-> a__U51(a__and(1 + z0, 1 + z1), z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__isNatList(z) -{ 0 }-> 2 :|: z = 1
   a__isNatList(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__isNatList(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__length(z) -{ 0 }-> a__U61(a__and(a__and(a__U51(a__and(a__isNatKind(z0312), 1 + z1134), z0312, z1134), 1 + (1 + z0312 + z1134)), 1 + (1 + z0) + (1 + z0)), 1 + z0312 + z1134) :|: z1134 >= 0, z = 1 + z0 + (1 + z0312 + z1134), z0 >= 0, z0312 >= 0
   a__length(z) -{ 0 }-> a__U61(a__and(a__and(2, 1 + 1), 1 + (1 + z0) + (1 + z0)), 1) :|: z0 >= 0, z = 1 + z0 + 1
   a__length(z) -{ 0 }-> a__U61(a__and(a__and(0, 1 + z1), 1 + (1 + z0) + (1 + z0)), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__length(z) -{ 0 }-> a__U61(a__and(a__and(1 + z1, 1 + z1), 1 + (1 + z0) + (1 + z0)), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__length(z) -{ 0 }-> 0 :|: z = 1
   a__length(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__length(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__zeros -{ 0 }-> 3 :|: 
   a__zeros -{ 0 }-> 0 :|: 
   a__zeros -{ 0 }-> 1 + 0 + 3 :|: 
   mark(z) -{ 0 }-> a__length(mark(z0)) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__isNatList(z0) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__isNatKind(z0) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__isNatIListKind(z0) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__isNatIList(z0) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__isNat(z0) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__and(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__U61(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__U53(mark(z0)) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__U52(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__U51(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U43(mark(z0)) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__U42(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__U41(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U32(mark(z0)) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__U31(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__U22(mark(z0)) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__U21(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__U12(mark(z0)) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__U11(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> 3 :|: z = 3
   mark(z) -{ 0 }-> 2 :|: z = 2
   mark(z) -{ 0 }-> 1 :|: z = 1
   mark(z) -{ 0 }-> 0 :|: z = 0
   mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   mark(z) -{ 0 }-> 0 :|: z = 3
   mark(z) -{ 0 }-> 1 + mark(z0) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> 1 + mark(z0) + z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> 1 + 0 + 3 :|: z = 3


----------------------------------------

(39) SimplificationProof (BOTH BOUNDS(ID, ID))
Simplified the RNTS by moving equalities from the constraints into the right-hand sides.
----------------------------------------

(40)
Obligation:
Complexity RNTS consisting of the following rules:

   A__AND(z, z') -{ 1 }-> 1 + MARK(z') :|: z = 2, z' >= 0
   A__ISNAT(z) -{ 1 }-> 1 + A__U21(a__isNatKind(z - 2), 1 + (z - 2)) + A__ISNATKIND(1 + (z - 2)) :|: z - 2 >= 0
   A__ISNAT(z) -{ 1 }-> 1 + A__U21(a__isNatIListKind(z - 2), 1 + (z - 2)) + A__ISNATKIND(1 + (z - 2)) :|: z - 2 >= 0
   A__ISNAT(z) -{ 1 }-> 1 + A__U21(2, 0) + A__ISNATKIND(0) :|: z = 1 + 0
   A__ISNAT(z) -{ 1 }-> 1 + A__U21(0, z - 1) + A__ISNATKIND(z - 1) :|: z - 1 >= 0
   A__ISNAT(z) -{ 1 }-> 1 + A__U21(1 + (z - 1), z - 1) + A__ISNATKIND(z - 1) :|: z - 1 >= 0
   A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(a__isNatKind(z025), 1 + z19), 1 + z025 + z19) + A__ISNATILISTKIND(1 + z025 + z19) :|: z025 >= 0, z = 1 + (1 + z025 + z19), z19 >= 0
   A__ISNAT(z) -{ 1 }-> 1 + A__U11(2, 3) + A__ISNATILISTKIND(3) :|: z = 1 + 3
   A__ISNAT(z) -{ 1 }-> 1 + A__U11(2, 1) + A__ISNATILISTKIND(1) :|: z = 1 + 1
   A__ISNAT(z) -{ 1 }-> 1 + A__U11(0, z - 1) + A__ISNATILISTKIND(z - 1) :|: z - 1 >= 0
   A__ISNAT(z) -{ 1 }-> 1 + A__U11(1 + (z - 1), z - 1) + A__ISNATILISTKIND(z - 1) :|: z - 1 >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U31(a__and(a__isNatKind(z028), 1 + z110), 1 + z028 + z110) + A__ISNATILISTKIND(1 + z028 + z110) :|: z110 >= 0, z = 1 + z028 + z110, z028 >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U31(2, 3) + A__ISNATILISTKIND(3) :|: z = 3
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U31(2, 1) + A__ISNATILISTKIND(1) :|: z = 1
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U31(0, z) + A__ISNATILISTKIND(z) :|: z >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U31(1 + z, z) + A__ISNATILISTKIND(z) :|: z >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(a__isNatKind(z030), 1 + z1), 1 + z030, z1) + A__AND(a__isNatKind(z030), 1 + z1) + A__ISNATKIND(1 + z030) :|: z1 >= 0, z = 1 + (1 + z030) + z1, z030 >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(a__isNatKind(z030), 1 + z1), 1 + z030, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(1 + z030) :|: z1 >= 0, z = 1 + (1 + z030) + z1, z030 >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(a__isNatKind(z030), 1 + z1), 1 + z030, z1) + A__AND(1 + (1 + z030), 1 + z1) + A__ISNATKIND(1 + z030) :|: z1 >= 0, z = 1 + (1 + z030) + z1, z030 >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(a__isNatIListKind(z029), 1 + z1), 1 + z029, z1) + A__AND(a__isNatIListKind(z029), 1 + z1) + A__ISNATKIND(1 + z029) :|: z029 >= 0, z = 1 + (1 + z029) + z1, z1 >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(a__isNatIListKind(z029), 1 + z1), 1 + z029, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(1 + z029) :|: z029 >= 0, z = 1 + (1 + z029) + z1, z1 >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(a__isNatIListKind(z029), 1 + z1), 1 + z029, z1) + A__AND(1 + (1 + z029), 1 + z1) + A__ISNATKIND(1 + z029) :|: z029 >= 0, z = 1 + (1 + z029) + z1, z1 >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(2, 1 + (z - 1)), 0, z - 1) + A__AND(2, 1 + (z - 1)) + A__ISNATKIND(0) :|: z - 1 >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(2, 1 + (z - 1)), 0, z - 1) + A__AND(0, 1 + (z - 1)) + A__ISNATKIND(0) :|: z - 1 >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(2, 1 + (z - 1)), 0, z - 1) + A__AND(1 + 0, 1 + (z - 1)) + A__ISNATKIND(0) :|: z - 1 >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(0, 1 + z1), z0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(0, 1 + z1), z0, z1) + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(0, 1 + z1), 1 + z033, z1) + A__AND(a__isNatIListKind(z033), 1 + z1) + A__ISNATKIND(1 + z033) :|: z1 >= 0, z = 1 + (1 + z033) + z1, z033 >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(0, 1 + z1), 1 + z034, z1) + A__AND(a__isNatKind(z034), 1 + z1) + A__ISNATKIND(1 + z034) :|: z1 >= 0, z034 >= 0, z = 1 + (1 + z034) + z1
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(0, 1 + (z - 1)), 0, z - 1) + A__AND(2, 1 + (z - 1)) + A__ISNATKIND(0) :|: z - 1 >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(1 + z0, 1 + z1), z0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(1 + z0, 1 + z1), z0, z1) + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(1 + 0, 1 + (z - 1)), 0, z - 1) + A__AND(2, 1 + (z - 1)) + A__ISNATKIND(0) :|: z - 1 >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(1 + (1 + z031), 1 + z1), 1 + z031, z1) + A__AND(a__isNatIListKind(z031), 1 + z1) + A__ISNATKIND(1 + z031) :|: z = 1 + (1 + z031) + z1, z031 >= 0, z1 >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(1 + (1 + z032), 1 + z1), 1 + z032, z1) + A__AND(a__isNatKind(z032), 1 + z1) + A__ISNATKIND(1 + z032) :|: z032 >= 0, z1 >= 0, z = 1 + (1 + z032) + z1
   A__ISNATILISTKIND(z) -{ 1 }-> 1 + A__AND(a__isNatKind(z036), 1 + z1) + A__ISNATKIND(1 + z036) :|: z036 >= 0, z1 >= 0, z = 1 + (1 + z036) + z1
   A__ISNATILISTKIND(z) -{ 1 }-> 1 + A__AND(a__isNatIListKind(z035), 1 + z1) + A__ISNATKIND(1 + z035) :|: z035 >= 0, z1 >= 0, z = 1 + (1 + z035) + z1
   A__ISNATILISTKIND(z) -{ 1 }-> 1 + A__AND(2, 1 + (z - 1)) + A__ISNATKIND(0) :|: z - 1 >= 0
   A__ISNATILISTKIND(z) -{ 1 }-> 1 + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__ISNATILISTKIND(z) -{ 1 }-> 1 + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__ISNATKIND(z) -{ 1 }-> 1 + A__ISNATKIND(z - 1) :|: z - 1 >= 0
   A__ISNATKIND(z) -{ 1 }-> 1 + A__ISNATILISTKIND(z - 1) :|: z - 1 >= 0
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(a__isNatKind(z038), 1 + z1), 1 + z038, z1) + A__AND(a__isNatKind(z038), 1 + z1) + A__ISNATKIND(1 + z038) :|: z1 >= 0, z = 1 + (1 + z038) + z1, z038 >= 0
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(a__isNatKind(z038), 1 + z1), 1 + z038, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(1 + z038) :|: z1 >= 0, z = 1 + (1 + z038) + z1, z038 >= 0
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(a__isNatKind(z038), 1 + z1), 1 + z038, z1) + A__AND(1 + (1 + z038), 1 + z1) + A__ISNATKIND(1 + z038) :|: z1 >= 0, z = 1 + (1 + z038) + z1, z038 >= 0
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(a__isNatIListKind(z037), 1 + z1), 1 + z037, z1) + A__AND(a__isNatIListKind(z037), 1 + z1) + A__ISNATKIND(1 + z037) :|: z1 >= 0, z = 1 + (1 + z037) + z1, z037 >= 0
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(a__isNatIListKind(z037), 1 + z1), 1 + z037, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(1 + z037) :|: z1 >= 0, z = 1 + (1 + z037) + z1, z037 >= 0
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(a__isNatIListKind(z037), 1 + z1), 1 + z037, z1) + A__AND(1 + (1 + z037), 1 + z1) + A__ISNATKIND(1 + z037) :|: z1 >= 0, z = 1 + (1 + z037) + z1, z037 >= 0
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(2, 1 + (z - 1)), 0, z - 1) + A__AND(2, 1 + (z - 1)) + A__ISNATKIND(0) :|: z - 1 >= 0
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(2, 1 + (z - 1)), 0, z - 1) + A__AND(0, 1 + (z - 1)) + A__ISNATKIND(0) :|: z - 1 >= 0
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(2, 1 + (z - 1)), 0, z - 1) + A__AND(1 + 0, 1 + (z - 1)) + A__ISNATKIND(0) :|: z - 1 >= 0
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(0, 1 + z1), z0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(0, 1 + z1), z0, z1) + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(0, 1 + z1), 1 + z041, z1) + A__AND(a__isNatIListKind(z041), 1 + z1) + A__ISNATKIND(1 + z041) :|: z1 >= 0, z041 >= 0, z = 1 + (1 + z041) + z1
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(0, 1 + z1), 1 + z042, z1) + A__AND(a__isNatKind(z042), 1 + z1) + A__ISNATKIND(1 + z042) :|: z042 >= 0, z1 >= 0, z = 1 + (1 + z042) + z1
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(0, 1 + (z - 1)), 0, z - 1) + A__AND(2, 1 + (z - 1)) + A__ISNATKIND(0) :|: z - 1 >= 0
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(1 + z0, 1 + z1), z0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(1 + z0, 1 + z1), z0, z1) + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(1 + 0, 1 + (z - 1)), 0, z - 1) + A__AND(2, 1 + (z - 1)) + A__ISNATKIND(0) :|: z - 1 >= 0
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(1 + (1 + z039), 1 + z1), 1 + z039, z1) + A__AND(a__isNatIListKind(z039), 1 + z1) + A__ISNATKIND(1 + z039) :|: z1 >= 0, z039 >= 0, z = 1 + (1 + z039) + z1
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(1 + (1 + z040), 1 + z1), 1 + z040, z1) + A__AND(a__isNatKind(z040), 1 + z1) + A__ISNATKIND(1 + z040) :|: z1 >= 0, z040 >= 0, z = 1 + (1 + z040) + z1
   A__LENGTH(z) -{ 1 }-> 1 + A__U61(a__and(a__and(a__isNatList(z1), 1 + z1), 1 + (1 + z0) + (1 + z0)), z1) + A__AND(a__and(a__isNatList(z1), 1 + z1), 1 + (1 + z0) + (1 + z0)) + A__AND(a__isNatList(z1), 1 + z1) + A__ISNATLIST(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__U11(z, z') -{ 1 }-> 1 + A__ISNATLIST(z') :|: z = 2, z' >= 0
   A__U21(z, z') -{ 1 }-> 1 + A__ISNAT(z') :|: z = 2, z' >= 0
   A__U31(z, z') -{ 1 }-> 1 + A__ISNATLIST(z') :|: z = 2, z' >= 0
   A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(a__U21(a__isNatKind(z' - 1), z' - 1), z'') + A__ISNAT(1 + (z' - 1)) :|: z = 2, z'' >= 0, z' - 1 >= 0
   A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(a__U11(a__isNatIListKind(z' - 1), z' - 1), z'') + A__ISNAT(1 + (z' - 1)) :|: z = 2, z'' >= 0, z' - 1 >= 0
   A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(2, z'') + A__ISNAT(0) :|: z = 2, z'' >= 0, z' = 0
   A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(0, z'') + A__ISNAT(z') :|: z = 2, z'' >= 0, z' >= 0
   A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(1 + z', z'') + A__ISNAT(z') :|: z = 2, z'' >= 0, z' >= 0
   A__U42(z, z') -{ 1 }-> 1 + A__ISNATILIST(z') :|: z = 2, z' >= 0
   A__U51(z, z', z'') -{ 1 }-> 1 + A__U52(a__U21(a__isNatKind(z' - 1), z' - 1), z'') + A__ISNAT(1 + (z' - 1)) :|: z = 2, z'' >= 0, z' - 1 >= 0
   A__U51(z, z', z'') -{ 1 }-> 1 + A__U52(a__U11(a__isNatIListKind(z' - 1), z' - 1), z'') + A__ISNAT(1 + (z' - 1)) :|: z = 2, z'' >= 0, z' - 1 >= 0
   A__U51(z, z', z'') -{ 1 }-> 1 + A__U52(2, z'') + A__ISNAT(0) :|: z = 2, z'' >= 0, z' = 0
   A__U51(z, z', z'') -{ 1 }-> 1 + A__U52(0, z'') + A__ISNAT(z') :|: z = 2, z'' >= 0, z' >= 0
   A__U51(z, z', z'') -{ 1 }-> 1 + A__U52(1 + z', z'') + A__ISNAT(z') :|: z = 2, z'' >= 0, z' >= 0
   A__U52(z, z') -{ 1 }-> 1 + A__ISNATLIST(z') :|: z = 2, z' >= 0
   A__U61(z, z') -{ 1 }-> 1 + A__LENGTH(mark(z')) + MARK(z') :|: z = 2, z' >= 0
   MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + MARK(z - 1) :|: z - 1 >= 0
   MARK(z) -{ 1 }-> 1 + A__ISNATLIST(z - 1) :|: z - 1 >= 0
   MARK(z) -{ 1 }-> 1 + A__ISNATKIND(z - 1) :|: z - 1 >= 0
   MARK(z) -{ 1 }-> 1 + A__ISNATILISTKIND(z - 1) :|: z - 1 >= 0
   MARK(z) -{ 1 }-> 1 + A__ISNATILIST(z - 1) :|: z - 1 >= 0
   MARK(z) -{ 1 }-> 1 + A__ISNAT(z - 1) :|: z - 1 >= 0
   MARK(z) -{ 1 }-> 1 + A__U61(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__U52(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__U51(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U42(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__U41(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U31(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__U21(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__U11(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__LENGTH(mark(z - 1)) + MARK(z - 1) :|: z - 1 >= 0
   MARK(z) -{ 1 }-> 1 + A__AND(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__U11(z, z') -{ 0 }-> a__U12(a__U51(a__and(a__isNatKind(z0270), 1 + z1118), z0270, z1118)) :|: z = 2, z' = 1 + z0270 + z1118, z0270 >= 0, z1118 >= 0
   a__U11(z, z') -{ 0 }-> 2 :|: z = 2, z' = 1, 2 = 2
   a__U11(z, z') -{ 0 }-> 2 :|: z = 2, z' >= 0, 1 + z' = 2
   a__U11(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   a__U11(z, z') -{ 0 }-> 0 :|: z = 2, z' = 1, v0 >= 0, 2 = v0
   a__U11(z, z') -{ 0 }-> 0 :|: z = 2, z' >= 0, v0 >= 0, 1 + z' = v0
   a__U11(z, z') -{ 0 }-> 0 :|: z = 2, z' >= 0, v0 >= 0, 0 = v0
   a__U11(z, z') -{ 0 }-> 1 + z0 :|: z = 2, z' = 1, 2 = z0, z0 >= 0
   a__U11(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z' >= 0, 1 + z' = z0', z0' >= 0
   a__U11(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z' >= 0, 0 = z0', z0' >= 0
   a__U11(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   a__U12(z) -{ 0 }-> 2 :|: z = 2
   a__U12(z) -{ 0 }-> 0 :|: z >= 0
   a__U12(z) -{ 0 }-> 1 + z :|: z >= 0
   a__U21(z, z') -{ 0 }-> a__U22(a__U21(a__isNatKind(z' - 1), z' - 1)) :|: z = 2, z' - 1 >= 0
   a__U21(z, z') -{ 0 }-> a__U22(a__U11(a__isNatIListKind(z' - 1), z' - 1)) :|: z = 2, z' - 1 >= 0
   a__U21(z, z') -{ 0 }-> 2 :|: z = 2, z' = 0, 2 = 2
   a__U21(z, z') -{ 0 }-> 2 :|: z = 2, z' >= 0, 1 + z' = 2
   a__U21(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   a__U21(z, z') -{ 0 }-> 0 :|: z = 2, z' = 0, v0 >= 0, 2 = v0
   a__U21(z, z') -{ 0 }-> 0 :|: z = 2, z' >= 0, v0 >= 0, 1 + z' = v0
   a__U21(z, z') -{ 0 }-> 0 :|: z = 2, z' >= 0, v0 >= 0, 0 = v0
   a__U21(z, z') -{ 0 }-> 1 + z0 :|: z = 2, z' = 0, 2 = z0, z0 >= 0
   a__U21(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z' >= 0, 1 + z' = z0', z0' >= 0
   a__U21(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z' >= 0, 0 = z0', z0' >= 0
   a__U21(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   a__U22(z) -{ 0 }-> 2 :|: z = 2
   a__U22(z) -{ 0 }-> 0 :|: z >= 0
   a__U22(z) -{ 0 }-> 1 + z :|: z >= 0
   a__U31(z, z') -{ 0 }-> a__U32(a__U51(a__and(a__isNatKind(z0273), 1 + z1119), z0273, z1119)) :|: z = 2, z0273 >= 0, z' = 1 + z0273 + z1119, z1119 >= 0
   a__U31(z, z') -{ 0 }-> 2 :|: z = 2, z' = 1, 2 = 2
   a__U31(z, z') -{ 0 }-> 2 :|: z = 2, z' >= 0, 1 + z' = 2
   a__U31(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   a__U31(z, z') -{ 0 }-> 0 :|: z = 2, z' = 1, v0 >= 0, 2 = v0
   a__U31(z, z') -{ 0 }-> 0 :|: z = 2, z' >= 0, v0 >= 0, 1 + z' = v0
   a__U31(z, z') -{ 0 }-> 0 :|: z = 2, z' >= 0, v0 >= 0, 0 = v0
   a__U31(z, z') -{ 0 }-> 1 + z0 :|: z = 2, z' = 1, 2 = z0, z0 >= 0
   a__U31(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z' >= 0, 1 + z' = z0', z0' >= 0
   a__U31(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z' >= 0, 0 = z0', z0' >= 0
   a__U31(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   a__U32(z) -{ 0 }-> 2 :|: z = 2
   a__U32(z) -{ 0 }-> 0 :|: z >= 0
   a__U32(z) -{ 0 }-> 1 + z :|: z >= 0
   a__U41(z, z', z'') -{ 0 }-> a__U42(a__U21(a__isNatKind(z' - 1), z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   a__U41(z, z', z'') -{ 0 }-> a__U42(a__U11(a__isNatIListKind(z' - 1), z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   a__U41(z, z', z'') -{ 0 }-> a__U42(2, z'') :|: z = 2, z'' >= 0, z' = 0
   a__U41(z, z', z'') -{ 0 }-> a__U42(0, z'') :|: z = 2, z'' >= 0, z' >= 0
   a__U41(z, z', z'') -{ 0 }-> a__U42(1 + z', z'') :|: z = 2, z'' >= 0, z' >= 0
   a__U41(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   a__U41(z, z', z'') -{ 0 }-> 1 + z + z' + z'' :|: z' >= 0, z >= 0, z'' >= 0
   a__U42(z, z') -{ 0 }-> a__U43(a__U41(a__and(a__isNatKind(z0276), 1 + z1120), z0276, z1120)) :|: z = 2, z0276 >= 0, z' = 1 + z0276 + z1120, z1120 >= 0
   a__U42(z, z') -{ 0 }-> a__U43(a__U31(a__isNatIListKind(z'), z')) :|: z = 2, z' >= 0
   a__U42(z, z') -{ 0 }-> 2 :|: z = 2, z' = 3, 2 = 2
   a__U42(z, z') -{ 0 }-> 2 :|: z = 2, z' >= 0, 1 + z' = 2
   a__U42(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   a__U42(z, z') -{ 0 }-> 0 :|: z = 2, z' = 3, v0 >= 0, 2 = v0
   a__U42(z, z') -{ 0 }-> 0 :|: z = 2, z' >= 0, v0 >= 0, 1 + z' = v0
   a__U42(z, z') -{ 0 }-> 0 :|: z = 2, z' >= 0, v0 >= 0, 0 = v0
   a__U42(z, z') -{ 0 }-> 1 + z0 :|: z = 2, z' = 3, 2 = z0, z0 >= 0
   a__U42(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z' >= 0, 1 + z' = z0', z0' >= 0
   a__U42(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z' >= 0, 0 = z0', z0' >= 0
   a__U42(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   a__U43(z) -{ 0 }-> 2 :|: z = 2
   a__U43(z) -{ 0 }-> 0 :|: z >= 0
   a__U43(z) -{ 0 }-> 1 + z :|: z >= 0
   a__U51(z, z', z'') -{ 0 }-> a__U52(a__U21(a__isNatKind(z' - 1), z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   a__U51(z, z', z'') -{ 0 }-> a__U52(a__U11(a__isNatIListKind(z' - 1), z' - 1), z'') :|: z = 2, z' - 1 >= 0, z'' >= 0
   a__U51(z, z', z'') -{ 0 }-> a__U52(2, z'') :|: z = 2, z'' >= 0, z' = 0
   a__U51(z, z', z'') -{ 0 }-> a__U52(0, z'') :|: z = 2, z'' >= 0, z' >= 0
   a__U51(z, z', z'') -{ 0 }-> a__U52(1 + z', z'') :|: z = 2, z'' >= 0, z' >= 0
   a__U51(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   a__U51(z, z', z'') -{ 0 }-> 1 + z + z' + z'' :|: z' >= 0, z >= 0, z'' >= 0
   a__U52(z, z') -{ 0 }-> a__U53(a__U51(a__and(a__isNatKind(z0279), 1 + z1121), z0279, z1121)) :|: z = 2, z0279 >= 0, z' = 1 + z0279 + z1121, z1121 >= 0
   a__U52(z, z') -{ 0 }-> 2 :|: z = 2, z' = 1, 2 = 2
   a__U52(z, z') -{ 0 }-> 2 :|: z = 2, z' >= 0, 1 + z' = 2
   a__U52(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   a__U52(z, z') -{ 0 }-> 0 :|: z = 2, z' = 1, v0 >= 0, 2 = v0
   a__U52(z, z') -{ 0 }-> 0 :|: z = 2, z' >= 0, v0 >= 0, 1 + z' = v0
   a__U52(z, z') -{ 0 }-> 0 :|: z = 2, z' >= 0, v0 >= 0, 0 = v0
   a__U52(z, z') -{ 0 }-> 1 + z0 :|: z = 2, z' = 1, 2 = z0, z0 >= 0
   a__U52(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z' >= 0, 1 + z' = z0', z0' >= 0
   a__U52(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z' >= 0, 0 = z0', z0' >= 0
   a__U52(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   a__U53(z) -{ 0 }-> 2 :|: z = 2
   a__U53(z) -{ 0 }-> 0 :|: z >= 0
   a__U53(z) -{ 0 }-> 1 + z :|: z >= 0
   a__U61(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   a__U61(z, z') -{ 0 }-> 1 + a__length(mark(z')) :|: z = 2, z' >= 0
   a__U61(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   a__and(z, z') -{ 0 }-> mark(z') :|: z = 2, z' >= 0
   a__and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   a__and(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   a__isNat(z) -{ 0 }-> a__U21(a__isNatKind(z - 2), 1 + (z - 2)) :|: z - 2 >= 0
   a__isNat(z) -{ 0 }-> a__U21(a__isNatIListKind(z - 2), 1 + (z - 2)) :|: z - 2 >= 0
   a__isNat(z) -{ 0 }-> a__U21(2, 0) :|: z = 1 + 0
   a__isNat(z) -{ 0 }-> a__U21(0, z - 1) :|: z - 1 >= 0
   a__isNat(z) -{ 0 }-> a__U21(1 + (z - 1), z - 1) :|: z - 1 >= 0
   a__isNat(z) -{ 0 }-> a__U11(a__and(a__isNatKind(z0302), 1 + z1132), 1 + z0302 + z1132) :|: z0302 >= 0, z = 1 + (1 + z0302 + z1132), z1132 >= 0
   a__isNat(z) -{ 0 }-> a__U11(2, 3) :|: z = 1 + 3
   a__isNat(z) -{ 0 }-> a__U11(2, 1) :|: z = 1 + 1
   a__isNat(z) -{ 0 }-> a__U11(0, z - 1) :|: z - 1 >= 0
   a__isNat(z) -{ 0 }-> a__U11(1 + (z - 1), z - 1) :|: z - 1 >= 0
   a__isNat(z) -{ 0 }-> 2 :|: z = 0
   a__isNat(z) -{ 0 }-> 0 :|: z >= 0
   a__isNat(z) -{ 0 }-> 1 + z :|: z >= 0
   a__isNatIList(z) -{ 0 }-> a__U41(a__and(a__isNatKind(z0307), 1 + z1), 1 + z0307, z1) :|: z1 >= 0, z0307 >= 0, z = 1 + (1 + z0307) + z1
   a__isNatIList(z) -{ 0 }-> a__U41(a__and(a__isNatIListKind(z0306), 1 + z1), 1 + z0306, z1) :|: z0306 >= 0, z1 >= 0, z = 1 + (1 + z0306) + z1
   a__isNatIList(z) -{ 0 }-> a__U41(a__and(2, 1 + (z - 1)), 0, z - 1) :|: z - 1 >= 0
   a__isNatIList(z) -{ 0 }-> a__U41(a__and(0, 1 + z1), z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__isNatIList(z) -{ 0 }-> a__U41(a__and(1 + z0, 1 + z1), z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__isNatIList(z) -{ 0 }-> a__U31(a__and(a__isNatKind(z0305), 1 + z1133), 1 + z0305 + z1133) :|: z = 1 + z0305 + z1133, z1133 >= 0, z0305 >= 0
   a__isNatIList(z) -{ 0 }-> a__U31(2, 3) :|: z = 3
   a__isNatIList(z) -{ 0 }-> a__U31(2, 1) :|: z = 1
   a__isNatIList(z) -{ 0 }-> a__U31(0, z) :|: z >= 0
   a__isNatIList(z) -{ 0 }-> a__U31(1 + z, z) :|: z >= 0
   a__isNatIList(z) -{ 0 }-> 2 :|: z = 3
   a__isNatIList(z) -{ 0 }-> 0 :|: z >= 0
   a__isNatIList(z) -{ 0 }-> 1 + z :|: z >= 0
   a__isNatIListKind(z) -{ 0 }-> a__and(a__isNatKind(z0309), 1 + z1) :|: z1 >= 0, z = 1 + (1 + z0309) + z1, z0309 >= 0
   a__isNatIListKind(z) -{ 0 }-> a__and(a__isNatIListKind(z0308), 1 + z1) :|: z1 >= 0, z0308 >= 0, z = 1 + (1 + z0308) + z1
   a__isNatIListKind(z) -{ 0 }-> a__and(2, 1 + (z - 1)) :|: z - 1 >= 0
   a__isNatIListKind(z) -{ 0 }-> a__and(0, 1 + z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__isNatIListKind(z) -{ 0 }-> a__and(1 + z0, 1 + z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__isNatIListKind(z) -{ 0 }-> 2 :|: z = 1
   a__isNatIListKind(z) -{ 0 }-> 2 :|: z = 3
   a__isNatIListKind(z) -{ 0 }-> 0 :|: z >= 0
   a__isNatIListKind(z) -{ 0 }-> 1 + z :|: z >= 0
   a__isNatKind(z) -{ 0 }-> a__isNatKind(z - 1) :|: z - 1 >= 0
   a__isNatKind(z) -{ 0 }-> a__isNatIListKind(z - 1) :|: z - 1 >= 0
   a__isNatKind(z) -{ 0 }-> 2 :|: z = 0
   a__isNatKind(z) -{ 0 }-> 0 :|: z >= 0
   a__isNatKind(z) -{ 0 }-> 1 + z :|: z >= 0
   a__isNatList(z) -{ 0 }-> a__U51(a__and(a__isNatKind(z0311), 1 + z1), 1 + z0311, z1) :|: z1 >= 0, z = 1 + (1 + z0311) + z1, z0311 >= 0
   a__isNatList(z) -{ 0 }-> a__U51(a__and(a__isNatIListKind(z0310), 1 + z1), 1 + z0310, z1) :|: z1 >= 0, z0310 >= 0, z = 1 + (1 + z0310) + z1
   a__isNatList(z) -{ 0 }-> a__U51(a__and(2, 1 + (z - 1)), 0, z - 1) :|: z - 1 >= 0
   a__isNatList(z) -{ 0 }-> a__U51(a__and(0, 1 + z1), z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__isNatList(z) -{ 0 }-> a__U51(a__and(1 + z0, 1 + z1), z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__isNatList(z) -{ 0 }-> 2 :|: z = 1
   a__isNatList(z) -{ 0 }-> 0 :|: z >= 0
   a__isNatList(z) -{ 0 }-> 1 + z :|: z >= 0
   a__length(z) -{ 0 }-> a__U61(a__and(a__and(a__U51(a__and(a__isNatKind(z0312), 1 + z1134), z0312, z1134), 1 + (1 + z0312 + z1134)), 1 + (1 + z0) + (1 + z0)), 1 + z0312 + z1134) :|: z1134 >= 0, z = 1 + z0 + (1 + z0312 + z1134), z0 >= 0, z0312 >= 0
   a__length(z) -{ 0 }-> a__U61(a__and(a__and(2, 1 + 1), 1 + (1 + (z - 2)) + (1 + (z - 2))), 1) :|: z - 2 >= 0
   a__length(z) -{ 0 }-> a__U61(a__and(a__and(0, 1 + z1), 1 + (1 + z0) + (1 + z0)), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__length(z) -{ 0 }-> a__U61(a__and(a__and(1 + z1, 1 + z1), 1 + (1 + z0) + (1 + z0)), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__length(z) -{ 0 }-> 0 :|: z = 1
   a__length(z) -{ 0 }-> 0 :|: z >= 0
   a__length(z) -{ 0 }-> 1 + z :|: z >= 0
   a__zeros -{ 0 }-> 3 :|: 
   a__zeros -{ 0 }-> 0 :|: 
   a__zeros -{ 0 }-> 1 + 0 + 3 :|: 
   mark(z) -{ 0 }-> a__length(mark(z - 1)) :|: z - 1 >= 0
   mark(z) -{ 0 }-> a__isNatList(z - 1) :|: z - 1 >= 0
   mark(z) -{ 0 }-> a__isNatKind(z - 1) :|: z - 1 >= 0
   mark(z) -{ 0 }-> a__isNatIListKind(z - 1) :|: z - 1 >= 0
   mark(z) -{ 0 }-> a__isNatIList(z - 1) :|: z - 1 >= 0
   mark(z) -{ 0 }-> a__isNat(z - 1) :|: z - 1 >= 0
   mark(z) -{ 0 }-> a__and(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__U61(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__U53(mark(z - 1)) :|: z - 1 >= 0
   mark(z) -{ 0 }-> a__U52(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__U51(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U43(mark(z - 1)) :|: z - 1 >= 0
   mark(z) -{ 0 }-> a__U42(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__U41(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U32(mark(z - 1)) :|: z - 1 >= 0
   mark(z) -{ 0 }-> a__U31(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__U22(mark(z - 1)) :|: z - 1 >= 0
   mark(z) -{ 0 }-> a__U21(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__U12(mark(z - 1)) :|: z - 1 >= 0
   mark(z) -{ 0 }-> a__U11(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> 3 :|: z = 3
   mark(z) -{ 0 }-> 2 :|: z = 2
   mark(z) -{ 0 }-> 1 :|: z = 1
   mark(z) -{ 0 }-> 0 :|: z = 0
   mark(z) -{ 0 }-> 0 :|: z >= 0
   mark(z) -{ 0 }-> 0 :|: z = 3
   mark(z) -{ 0 }-> 1 + mark(z - 1) :|: z - 1 >= 0
   mark(z) -{ 0 }-> 1 + mark(z0) + z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> 1 + 0 + 3 :|: z = 3


----------------------------------------

(41) CompletionProof (UPPER BOUND(ID))
The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added:

   a__zeros -> null_a__zeros [0]
   a__U11(v0, v1) -> null_a__U11 [0]
   a__U12(v0) -> null_a__U12 [0]
   a__U21(v0, v1) -> null_a__U21 [0]
   a__U22(v0) -> null_a__U22 [0]
   a__U31(v0, v1) -> null_a__U31 [0]
   a__U32(v0) -> null_a__U32 [0]
   a__U41(v0, v1, v2) -> null_a__U41 [0]
   a__U42(v0, v1) -> null_a__U42 [0]
   a__U43(v0) -> null_a__U43 [0]
   a__U51(v0, v1, v2) -> null_a__U51 [0]
   a__U52(v0, v1) -> null_a__U52 [0]
   a__U53(v0) -> null_a__U53 [0]
   a__U61(v0, v1) -> null_a__U61 [0]
   a__and(v0, v1) -> null_a__and [0]
   a__isNat(v0) -> null_a__isNat [0]
   a__isNatIList(v0) -> null_a__isNatIList [0]
   a__isNatIListKind(v0) -> null_a__isNatIListKind [0]
   a__isNatKind(v0) -> null_a__isNatKind [0]
   a__isNatList(v0) -> null_a__isNatList [0]
   a__length(v0) -> null_a__length [0]
   mark(v0) -> null_mark [0]
   A__U41(v0, v1, v2) -> null_A__U41 [0]
   A__U51(v0, v1, v2) -> null_A__U51 [0]
   A__U61(v0, v1) -> null_A__U61 [0]
   A__AND(v0, v1) -> null_A__AND [0]
   A__ISNAT(v0) -> null_A__ISNAT [0]
   A__ISNATILISTKIND(v0) -> null_A__ISNATILISTKIND [0]
   A__ISNATKIND(v0) -> null_A__ISNATKIND [0]
   A__ISNATLIST(v0) -> null_A__ISNATLIST [0]
   A__LENGTH(v0) -> null_A__LENGTH [0]
   MARK(v0) -> null_MARK [0]
   A__U11(v0, v1) -> null_A__U11 [0]
   A__U21(v0, v1) -> null_A__U21 [0]
   A__U31(v0, v1) -> null_A__U31 [0]
   A__U42(v0, v1) -> null_A__U42 [0]
   A__U52(v0, v1) -> null_A__U52 [0]

And the following fresh constants:    null_a__zeros, null_a__U11, null_a__U12, null_a__U21, null_a__U22, null_a__U31, null_a__U32, null_a__U41, null_a__U42, null_a__U43, null_a__U51, null_a__U52, null_a__U53, null_a__U61, null_a__and, null_a__isNat, null_a__isNatIList, null_a__isNatIListKind, null_a__isNatKind, null_a__isNatList, null_a__length, null_mark, null_A__U41, null_A__U51, null_A__U61, null_A__AND, null_A__ISNAT, null_A__ISNATILISTKIND, null_A__ISNATKIND, null_A__ISNATLIST, null_A__LENGTH, null_MARK, null_A__U11, null_A__U21, null_A__U31, null_A__U42, null_A__U52, const

----------------------------------------

(42)
Obligation:
Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is:

Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   A__U41(tt, z0, z1) -> c14(A__U42(a__isNat(z0), z1), A__ISNAT(z0)) [1]
   A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0)) [1]
   A__U61(tt, z0) -> c26(A__LENGTH(mark(z0)), MARK(z0)) [1]
   A__AND(tt, z0) -> c28(MARK(z0)) [1]
   A__ISNAT(length(z0)) -> c31(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) [1]
   A__ISNAT(s(z0)) -> c32(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) [1]
   A__ISNATILIST(z0) -> c34(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) [1]
   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)) [1]
   A__ISNATILISTKIND(cons(z0, z1)) -> c40(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) [1]
   A__ISNATKIND(length(z0)) -> c43(A__ISNATILISTKIND(z0)) [1]
   A__ISNATKIND(s(z0)) -> c44(A__ISNATKIND(z0)) [1]
   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)) [1]
   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)) [1]
   MARK(U11(z0, z1)) -> c53(A__U11(mark(z0), z1), MARK(z0)) [1]
   MARK(isNatList(z0)) -> c55(A__ISNATLIST(z0)) [1]
   MARK(U21(z0, z1)) -> c56(A__U21(mark(z0), z1), MARK(z0)) [1]
   MARK(isNat(z0)) -> c58(A__ISNAT(z0)) [1]
   MARK(U31(z0, z1)) -> c59(A__U31(mark(z0), z1), MARK(z0)) [1]
   MARK(U41(z0, z1, z2)) -> c61(A__U41(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(U42(z0, z1)) -> c62(A__U42(mark(z0), z1), MARK(z0)) [1]
   MARK(isNatIList(z0)) -> c64(A__ISNATILIST(z0)) [1]
   MARK(U51(z0, z1, z2)) -> c65(A__U51(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(U52(z0, z1)) -> c66(A__U52(mark(z0), z1), MARK(z0)) [1]
   MARK(U61(z0, z1)) -> c68(A__U61(mark(z0), z1), MARK(z0)) [1]
   MARK(length(z0)) -> c69(A__LENGTH(mark(z0)), MARK(z0)) [1]
   MARK(and(z0, z1)) -> c70(A__AND(mark(z0), z1), MARK(z0)) [1]
   MARK(isNatIListKind(z0)) -> c71(A__ISNATILISTKIND(z0)) [1]
   MARK(isNatKind(z0)) -> c72(A__ISNATKIND(z0)) [1]
   MARK(cons(z0, z1)) -> c73(MARK(z0)) [1]
   MARK(s(z0)) -> c76(MARK(z0)) [1]
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) [1]
   A__U21(tt, z0) -> c6(A__ISNAT(z0)) [1]
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) [1]
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) [1]
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) [1]
   MARK(U12(z0)) -> c54(MARK(z0)) [1]
   MARK(U22(z0)) -> c57(MARK(z0)) [1]
   MARK(U32(z0)) -> c60(MARK(z0)) [1]
   MARK(U43(z0)) -> c63(MARK(z0)) [1]
   MARK(U53(z0)) -> c67(MARK(z0)) [1]
   a__zeros -> cons(0, zeros) [0]
   a__zeros -> zeros [0]
   a__U11(tt, z0) -> a__U12(a__isNatList(z0)) [0]
   a__U11(z0, z1) -> U11(z0, z1) [0]
   a__U12(tt) -> tt [0]
   a__U12(z0) -> U12(z0) [0]
   a__U21(tt, z0) -> a__U22(a__isNat(z0)) [0]
   a__U21(z0, z1) -> U21(z0, z1) [0]
   a__U22(tt) -> tt [0]
   a__U22(z0) -> U22(z0) [0]
   a__U31(tt, z0) -> a__U32(a__isNatList(z0)) [0]
   a__U31(z0, z1) -> U31(z0, z1) [0]
   a__U32(tt) -> tt [0]
   a__U32(z0) -> U32(z0) [0]
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) [0]
   a__U41(z0, z1, z2) -> U41(z0, z1, z2) [0]
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) [0]
   a__U42(z0, z1) -> U42(z0, z1) [0]
   a__U43(tt) -> tt [0]
   a__U43(z0) -> U43(z0) [0]
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) [0]
   a__U51(z0, z1, z2) -> U51(z0, z1, z2) [0]
   a__U52(tt, z0) -> a__U53(a__isNatList(z0)) [0]
   a__U52(z0, z1) -> U52(z0, z1) [0]
   a__U53(tt) -> tt [0]
   a__U53(z0) -> U53(z0) [0]
   a__U61(tt, z0) -> s(a__length(mark(z0))) [0]
   a__U61(z0, z1) -> U61(z0, z1) [0]
   a__and(tt, z0) -> mark(z0) [0]
   a__and(z0, z1) -> and(z0, z1) [0]
   a__isNat(0) -> tt [0]
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) [0]
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) [0]
   a__isNat(z0) -> isNat(z0) [0]
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) [0]
   a__isNatIList(zeros) -> tt [0]
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) [0]
   a__isNatIList(z0) -> isNatIList(z0) [0]
   a__isNatIListKind(nil) -> tt [0]
   a__isNatIListKind(zeros) -> tt [0]
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) [0]
   a__isNatIListKind(z0) -> isNatIListKind(z0) [0]
   a__isNatKind(0) -> tt [0]
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0) [0]
   a__isNatKind(s(z0)) -> a__isNatKind(z0) [0]
   a__isNatKind(z0) -> isNatKind(z0) [0]
   a__isNatList(nil) -> tt [0]
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) [0]
   a__isNatList(z0) -> isNatList(z0) [0]
   a__length(nil) -> 0 [0]
   a__length(cons(z0, z1)) -> a__U61(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) [0]
   a__length(z0) -> length(z0) [0]
   mark(zeros) -> a__zeros [0]
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1) [0]
   mark(U12(z0)) -> a__U12(mark(z0)) [0]
   mark(isNatList(z0)) -> a__isNatList(z0) [0]
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1) [0]
   mark(U22(z0)) -> a__U22(mark(z0)) [0]
   mark(isNat(z0)) -> a__isNat(z0) [0]
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1) [0]
   mark(U32(z0)) -> a__U32(mark(z0)) [0]
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) [0]
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1) [0]
   mark(U43(z0)) -> a__U43(mark(z0)) [0]
   mark(isNatIList(z0)) -> a__isNatIList(z0) [0]
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) [0]
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1) [0]
   mark(U53(z0)) -> a__U53(mark(z0)) [0]
   mark(U61(z0, z1)) -> a__U61(mark(z0), z1) [0]
   mark(length(z0)) -> a__length(mark(z0)) [0]
   mark(and(z0, z1)) -> a__and(mark(z0), z1) [0]
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) [0]
   mark(isNatKind(z0)) -> a__isNatKind(z0) [0]
   mark(cons(z0, z1)) -> cons(mark(z0), z1) [0]
   mark(0) -> 0 [0]
   mark(tt) -> tt [0]
   mark(s(z0)) -> s(mark(z0)) [0]
   mark(nil) -> nil [0]
   a__zeros -> null_a__zeros [0]
   a__U11(v0, v1) -> null_a__U11 [0]
   a__U12(v0) -> null_a__U12 [0]
   a__U21(v0, v1) -> null_a__U21 [0]
   a__U22(v0) -> null_a__U22 [0]
   a__U31(v0, v1) -> null_a__U31 [0]
   a__U32(v0) -> null_a__U32 [0]
   a__U41(v0, v1, v2) -> null_a__U41 [0]
   a__U42(v0, v1) -> null_a__U42 [0]
   a__U43(v0) -> null_a__U43 [0]
   a__U51(v0, v1, v2) -> null_a__U51 [0]
   a__U52(v0, v1) -> null_a__U52 [0]
   a__U53(v0) -> null_a__U53 [0]
   a__U61(v0, v1) -> null_a__U61 [0]
   a__and(v0, v1) -> null_a__and [0]
   a__isNat(v0) -> null_a__isNat [0]
   a__isNatIList(v0) -> null_a__isNatIList [0]
   a__isNatIListKind(v0) -> null_a__isNatIListKind [0]
   a__isNatKind(v0) -> null_a__isNatKind [0]
   a__isNatList(v0) -> null_a__isNatList [0]
   a__length(v0) -> null_a__length [0]
   mark(v0) -> null_mark [0]
   A__U41(v0, v1, v2) -> null_A__U41 [0]
   A__U51(v0, v1, v2) -> null_A__U51 [0]
   A__U61(v0, v1) -> null_A__U61 [0]
   A__AND(v0, v1) -> null_A__AND [0]
   A__ISNAT(v0) -> null_A__ISNAT [0]
   A__ISNATILISTKIND(v0) -> null_A__ISNATILISTKIND [0]
   A__ISNATKIND(v0) -> null_A__ISNATKIND [0]
   A__ISNATLIST(v0) -> null_A__ISNATLIST [0]
   A__LENGTH(v0) -> null_A__LENGTH [0]
   MARK(v0) -> null_MARK [0]
   A__U11(v0, v1) -> null_A__U11 [0]
   A__U21(v0, v1) -> null_A__U21 [0]
   A__U31(v0, v1) -> null_A__U31 [0]
   A__U42(v0, v1) -> null_A__U42 [0]
   A__U52(v0, v1) -> null_A__U52 [0]

The TRS has the following type information:
A__U41 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c14:null_A__U41
tt :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c14 :: c16:null_A__U42 -> c31:c32:null_A__ISNAT -> c14:null_A__U41
A__U42 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c16:null_A__U42
a__isNat :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
A__ISNAT :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c31:c32:null_A__ISNAT
A__U51 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c20:null_A__U51
c20 :: c22:null_A__U52 -> c31:c32:null_A__ISNAT -> c20:null_A__U51
A__U52 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c22:null_A__U52
A__U61 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c26:null_A__U61
c26 :: c50:null_A__LENGTH -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67:null_MARK -> c26:null_A__U61
A__LENGTH :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c50:null_A__LENGTH
mark :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
MARK :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67:null_MARK
A__AND :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c28:null_A__AND
c28 :: c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67:null_MARK -> c28:null_A__AND
length :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c31 :: c2:null_A__U11 -> c40:null_A__ISNATILISTKIND -> c31:c32:null_A__ISNAT
A__U11 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c2:null_A__U11
a__isNatIListKind :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
A__ISNATILISTKIND :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c40:null_A__ISNATILISTKIND
s :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c32 :: c6:null_A__U21 -> c43:c44:null_A__ISNATKIND -> c31:c32:null_A__ISNAT
A__U21 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c6:null_A__U21
a__isNatKind :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
A__ISNATKIND :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c43:c44:null_A__ISNATKIND
A__ISNATILIST :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c34:c36
c34 :: c10:null_A__U31 -> c40:null_A__ISNATILISTKIND -> c34:c36
A__U31 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c10:null_A__U31
cons :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c36 :: c14:null_A__U41 -> c28:null_A__AND -> c43:c44:null_A__ISNATKIND -> c34:c36
a__and :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
isNatIListKind :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c40 :: c28:null_A__AND -> c43:c44:null_A__ISNATKIND -> c40:null_A__ISNATILISTKIND
c43 :: c40:null_A__ISNATILISTKIND -> c43:c44:null_A__ISNATKIND
c44 :: c43:c44:null_A__ISNATKIND -> c43:c44:null_A__ISNATKIND
A__ISNATLIST :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> c47:null_A__ISNATLIST
c47 :: c20:null_A__U51 -> c28:null_A__AND -> c43:c44:null_A__ISNATKIND -> c47:null_A__ISNATLIST
c50 :: c26:null_A__U61 -> c28:null_A__AND -> c28:null_A__AND -> c47:null_A__ISNATLIST -> c50:null_A__LENGTH
a__isNatList :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
and :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
isNat :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
isNatKind :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
U11 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c53 :: c2:null_A__U11 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67:null_MARK -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67:null_MARK
isNatList :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c55 :: c47:null_A__ISNATLIST -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67:null_MARK
U21 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c56 :: c6:null_A__U21 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67:null_MARK -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67:null_MARK
c58 :: c31:c32:null_A__ISNAT -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67:null_MARK
U31 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c59 :: c10:null_A__U31 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67:null_MARK -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67:null_MARK
U41 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c61 :: c14:null_A__U41 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67:null_MARK -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67:null_MARK
U42 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c62 :: c16:null_A__U42 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67:null_MARK -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67:null_MARK
isNatIList :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c64 :: c34:c36 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67:null_MARK
U51 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c65 :: c20:null_A__U51 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67:null_MARK -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67:null_MARK
U52 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c66 :: c22:null_A__U52 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67:null_MARK -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67:null_MARK
U61 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c68 :: c26:null_A__U61 -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67:null_MARK -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67:null_MARK
c69 :: c50:null_A__LENGTH -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67:null_MARK -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67:null_MARK
c70 :: c28:null_A__AND -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67:null_MARK -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67:null_MARK
c71 :: c40:null_A__ISNATILISTKIND -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67:null_MARK
c72 :: c43:c44:null_A__ISNATKIND -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67:null_MARK
c73 :: c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67:null_MARK -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67:null_MARK
c76 :: c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67:null_MARK -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67:null_MARK
c2 :: c47:null_A__ISNATLIST -> c2:null_A__U11
c6 :: c31:c32:null_A__ISNAT -> c6:null_A__U21
c10 :: c47:null_A__ISNATLIST -> c10:null_A__U31
c16 :: c34:c36 -> c16:null_A__U42
c22 :: c47:null_A__ISNATLIST -> c22:null_A__U52
U12 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c54 :: c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67:null_MARK -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67:null_MARK
U22 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c57 :: c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67:null_MARK -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67:null_MARK
U32 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c60 :: c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67:null_MARK -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67:null_MARK
U43 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c63 :: c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67:null_MARK -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67:null_MARK
U53 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
c67 :: c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67:null_MARK -> c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67:null_MARK
a__zeros :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
0 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
zeros :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__U11 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__U12 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__U21 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__U22 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__U31 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__U32 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__U41 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__U42 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__U43 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__isNatIList :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__U51 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__U52 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__U53 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__U61 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
a__length :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark -> tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
nil :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__zeros :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__U11 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__U12 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__U21 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__U22 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__U31 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__U32 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__U41 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__U42 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__U43 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__U51 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__U52 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__U53 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__U61 :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__and :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__isNat :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__isNatIList :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__isNatIListKind :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__isNatKind :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__isNatList :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_a__length :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_mark :: tt:length:s:cons:isNatIListKind:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U12:U22:U32:U43:U53:0:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_mark
null_A__U41 :: c14:null_A__U41
null_A__U51 :: c20:null_A__U51
null_A__U61 :: c26:null_A__U61
null_A__AND :: c28:null_A__AND
null_A__ISNAT :: c31:c32:null_A__ISNAT
null_A__ISNATILISTKIND :: c40:null_A__ISNATILISTKIND
null_A__ISNATKIND :: c43:c44:null_A__ISNATKIND
null_A__ISNATLIST :: c47:null_A__ISNATLIST
null_A__LENGTH :: c50:null_A__LENGTH
null_MARK :: c53:c55:c56:c58:c59:c61:c62:c64:c65:c66:c68:c69:c70:c71:c72:c73:c76:c54:c57:c60:c63:c67:null_MARK
null_A__U11 :: c2:null_A__U11
null_A__U21 :: c6:null_A__U21
null_A__U31 :: c10:null_A__U31
null_A__U42 :: c16:null_A__U42
null_A__U52 :: c22:null_A__U52
const :: c34:c36

Rewrite Strategy: INNERMOST
----------------------------------------

(43) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID))
Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction.
The constant constructors are abstracted as follows:

   tt => 2
   0 => 0
   zeros => 3
   nil => 1
   null_a__zeros => 0
   null_a__U11 => 0
   null_a__U12 => 0
   null_a__U21 => 0
   null_a__U22 => 0
   null_a__U31 => 0
   null_a__U32 => 0
   null_a__U41 => 0
   null_a__U42 => 0
   null_a__U43 => 0
   null_a__U51 => 0
   null_a__U52 => 0
   null_a__U53 => 0
   null_a__U61 => 0
   null_a__and => 0
   null_a__isNat => 0
   null_a__isNatIList => 0
   null_a__isNatIListKind => 0
   null_a__isNatKind => 0
   null_a__isNatList => 0
   null_a__length => 0
   null_mark => 0
   null_A__U41 => 0
   null_A__U51 => 0
   null_A__U61 => 0
   null_A__AND => 0
   null_A__ISNAT => 0
   null_A__ISNATILISTKIND => 0
   null_A__ISNATKIND => 0
   null_A__ISNATLIST => 0
   null_A__LENGTH => 0
   null_MARK => 0
   null_A__U11 => 0
   null_A__U21 => 0
   null_A__U31 => 0
   null_A__U42 => 0
   null_A__U52 => 0
   const => 0

----------------------------------------

(44)
Obligation:
Complexity RNTS consisting of the following rules:

   A__AND(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   A__AND(z, z') -{ 1 }-> 1 + MARK(z0) :|: z = 2, z0 >= 0, z' = z0
   A__ISNAT(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   A__ISNAT(z) -{ 1 }-> 1 + A__U21(a__isNatKind(z0), z0) + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0
   A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__isNatIListKind(z0), z0) + A__ISNATILISTKIND(z0) :|: z = 1 + z0, z0 >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U31(a__isNatIListKind(z0), z0) + A__ISNATILISTKIND(z0) :|: z = z0, z0 >= 0
   A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(a__isNatKind(z0), 1 + z1), z0, z1) + A__AND(a__isNatKind(z0), 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__ISNATILISTKIND(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   A__ISNATILISTKIND(z) -{ 1 }-> 1 + A__AND(a__isNatKind(z0), 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__ISNATKIND(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   A__ISNATKIND(z) -{ 1 }-> 1 + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0
   A__ISNATKIND(z) -{ 1 }-> 1 + A__ISNATILISTKIND(z0) :|: z = 1 + z0, z0 >= 0
   A__ISNATLIST(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(a__isNatKind(z0), 1 + z1), z0, z1) + A__AND(a__isNatKind(z0), 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__LENGTH(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   A__LENGTH(z) -{ 1 }-> 1 + A__U61(a__and(a__and(a__isNatList(z1), 1 + z1), 1 + (1 + z0) + (1 + z0)), z1) + A__AND(a__and(a__isNatList(z1), 1 + z1), 1 + (1 + z0) + (1 + z0)) + A__AND(a__isNatList(z1), 1 + z1) + A__ISNATLIST(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__U11(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   A__U11(z, z') -{ 1 }-> 1 + A__ISNATLIST(z0) :|: z = 2, z0 >= 0, z' = z0
   A__U21(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   A__U21(z, z') -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 2, z0 >= 0, z' = z0
   A__U31(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   A__U31(z, z') -{ 1 }-> 1 + A__ISNATLIST(z0) :|: z = 2, z0 >= 0, z' = z0
   A__U41(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(a__isNat(z0), z1) + A__ISNAT(z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1
   A__U42(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   A__U42(z, z') -{ 1 }-> 1 + A__ISNATILIST(z0) :|: z = 2, z0 >= 0, z' = z0
   A__U51(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   A__U51(z, z', z'') -{ 1 }-> 1 + A__U52(a__isNat(z0), z1) + A__ISNAT(z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1
   A__U52(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   A__U52(z, z') -{ 1 }-> 1 + A__ISNATLIST(z0) :|: z = 2, z0 >= 0, z' = z0
   A__U61(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   A__U61(z, z') -{ 1 }-> 1 + A__LENGTH(mark(z0)) + MARK(z0) :|: z = 2, z0 >= 0, z' = z0
   MARK(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0
   MARK(z) -{ 1 }-> 1 + A__ISNATLIST(z0) :|: z = 1 + z0, z0 >= 0
   MARK(z) -{ 1 }-> 1 + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0
   MARK(z) -{ 1 }-> 1 + A__ISNATILISTKIND(z0) :|: z = 1 + z0, z0 >= 0
   MARK(z) -{ 1 }-> 1 + A__ISNATILIST(z0) :|: z = 1 + z0, z0 >= 0
   MARK(z) -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1 + z0, z0 >= 0
   MARK(z) -{ 1 }-> 1 + A__U61(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__U52(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__U51(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U42(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__U41(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U31(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__U21(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__U11(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__LENGTH(mark(z0)) + MARK(z0) :|: z = 1 + z0, z0 >= 0
   MARK(z) -{ 1 }-> 1 + A__AND(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__U11(z, z') -{ 0 }-> a__U12(a__isNatList(z0)) :|: z = 2, z0 >= 0, z' = z0
   a__U11(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   a__U11(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   a__U12(z) -{ 0 }-> 2 :|: z = 2
   a__U12(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__U12(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__U21(z, z') -{ 0 }-> a__U22(a__isNat(z0)) :|: z = 2, z0 >= 0, z' = z0
   a__U21(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   a__U21(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   a__U22(z) -{ 0 }-> 2 :|: z = 2
   a__U22(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__U22(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__U31(z, z') -{ 0 }-> a__U32(a__isNatList(z0)) :|: z = 2, z0 >= 0, z' = z0
   a__U31(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   a__U31(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   a__U32(z) -{ 0 }-> 2 :|: z = 2
   a__U32(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__U32(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__U41(z, z', z'') -{ 0 }-> a__U42(a__isNat(z0), z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1
   a__U41(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   a__U41(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0
   a__U42(z, z') -{ 0 }-> a__U43(a__isNatIList(z0)) :|: z = 2, z0 >= 0, z' = z0
   a__U42(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   a__U42(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   a__U43(z) -{ 0 }-> 2 :|: z = 2
   a__U43(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__U43(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__U51(z, z', z'') -{ 0 }-> a__U52(a__isNat(z0), z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1
   a__U51(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   a__U51(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0
   a__U52(z, z') -{ 0 }-> a__U53(a__isNatList(z0)) :|: z = 2, z0 >= 0, z' = z0
   a__U52(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   a__U52(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   a__U53(z) -{ 0 }-> 2 :|: z = 2
   a__U53(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__U53(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__U61(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   a__U61(z, z') -{ 0 }-> 1 + a__length(mark(z0)) :|: z = 2, z0 >= 0, z' = z0
   a__U61(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   a__and(z, z') -{ 0 }-> mark(z0) :|: z = 2, z0 >= 0, z' = z0
   a__and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   a__and(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   a__isNat(z) -{ 0 }-> a__U21(a__isNatKind(z0), z0) :|: z = 1 + z0, z0 >= 0
   a__isNat(z) -{ 0 }-> a__U11(a__isNatIListKind(z0), z0) :|: z = 1 + z0, z0 >= 0
   a__isNat(z) -{ 0 }-> 2 :|: z = 0
   a__isNat(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__isNat(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__isNatIList(z) -{ 0 }-> a__U41(a__and(a__isNatKind(z0), 1 + z1), z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__isNatIList(z) -{ 0 }-> a__U31(a__isNatIListKind(z0), z0) :|: z = z0, z0 >= 0
   a__isNatIList(z) -{ 0 }-> 2 :|: z = 3
   a__isNatIList(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__isNatIList(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__isNatIListKind(z) -{ 0 }-> a__and(a__isNatKind(z0), 1 + z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__isNatIListKind(z) -{ 0 }-> 2 :|: z = 1
   a__isNatIListKind(z) -{ 0 }-> 2 :|: z = 3
   a__isNatIListKind(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__isNatIListKind(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__isNatKind(z) -{ 0 }-> a__isNatKind(z0) :|: z = 1 + z0, z0 >= 0
   a__isNatKind(z) -{ 0 }-> a__isNatIListKind(z0) :|: z = 1 + z0, z0 >= 0
   a__isNatKind(z) -{ 0 }-> 2 :|: z = 0
   a__isNatKind(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__isNatKind(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__isNatList(z) -{ 0 }-> a__U51(a__and(a__isNatKind(z0), 1 + z1), z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__isNatList(z) -{ 0 }-> 2 :|: z = 1
   a__isNatList(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__isNatList(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__length(z) -{ 0 }-> a__U61(a__and(a__and(a__isNatList(z1), 1 + z1), 1 + (1 + z0) + (1 + z0)), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__length(z) -{ 0 }-> 0 :|: z = 1
   a__length(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__length(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__zeros -{ 0 }-> 3 :|: 
   a__zeros -{ 0 }-> 0 :|: 
   a__zeros -{ 0 }-> 1 + 0 + 3 :|: 
   mark(z) -{ 0 }-> a__zeros :|: z = 3
   mark(z) -{ 0 }-> a__length(mark(z0)) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__isNatList(z0) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__isNatKind(z0) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__isNatIListKind(z0) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__isNatIList(z0) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__isNat(z0) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__and(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__U61(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__U53(mark(z0)) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__U52(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__U51(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U43(mark(z0)) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__U42(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__U41(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U32(mark(z0)) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__U31(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__U22(mark(z0)) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__U21(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__U12(mark(z0)) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__U11(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> 2 :|: z = 2
   mark(z) -{ 0 }-> 1 :|: z = 1
   mark(z) -{ 0 }-> 0 :|: z = 0
   mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   mark(z) -{ 0 }-> 1 + mark(z0) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> 1 + mark(z0) + z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1

Only complete derivations are relevant for the runtime complexity.

----------------------------------------

(45) 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))

----------------------------------------

(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__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


----------------------------------------

(47) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(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__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


----------------------------------------

(49) 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))

----------------------------------------

(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__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


----------------------------------------

(51) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(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__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


----------------------------------------

(53) 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))

----------------------------------------

(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__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


----------------------------------------

(55) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing nodes:
   A__U61(tt, nil) -> c26(A__LENGTH(nil), MARK(nil))
   A__U61(tt, 0) -> c26(A__LENGTH(0), MARK(0))
   A__U61(tt, tt) -> c26(A__LENGTH(tt), MARK(tt))

----------------------------------------

(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__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


----------------------------------------

(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__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


----------------------------------------

(59) 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))

----------------------------------------

(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__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


----------------------------------------

(61) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 3 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__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


----------------------------------------

(63) 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))

----------------------------------------

(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__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


----------------------------------------

(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__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


----------------------------------------

(67) 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))

----------------------------------------

(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__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


----------------------------------------

(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__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


----------------------------------------

(71) 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))

----------------------------------------

(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__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


----------------------------------------

(73) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(74)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0) -> 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


----------------------------------------

(75) 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))

----------------------------------------

(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))
   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


----------------------------------------

(77) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(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))
   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


----------------------------------------

(79) 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))

----------------------------------------

(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))
   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


----------------------------------------

(81) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 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))
   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


----------------------------------------

(83) 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))

----------------------------------------

(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(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


----------------------------------------

(85) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing tuple parts
----------------------------------------

(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(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


----------------------------------------

(87) 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))

----------------------------------------

(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(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


----------------------------------------

(89) 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))

----------------------------------------

(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(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


----------------------------------------

(91) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 4 trailing tuple parts
----------------------------------------

(92)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0) -> 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


----------------------------------------

(93) 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))

----------------------------------------

(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(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


----------------------------------------

(95) 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))

----------------------------------------

(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(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


----------------------------------------

(97) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 4 trailing tuple parts
----------------------------------------

(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(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


----------------------------------------

(99) 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))

----------------------------------------

(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(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


----------------------------------------

(101) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   MARK(U31(0, x1)) -> c59(A__U31(0, x1), MARK(0))
   MARK(U31(nil, x1)) -> c59(A__U31(nil, x1), 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(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


----------------------------------------

(103) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 4 trailing tuple parts
----------------------------------------

(104)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0) -> 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


----------------------------------------

(105) 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))

----------------------------------------

(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(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


----------------------------------------

(107) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   MARK(U41(0, x1, x2)) -> c61(A__U41(0, x1, x2), MARK(0))
   MARK(U41(nil, x1, x2)) -> c61(A__U41(nil, x1, x2), 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(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


----------------------------------------

(109) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 4 trailing tuple parts
----------------------------------------

(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(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))
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   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


----------------------------------------

(111) 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))

----------------------------------------

(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(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)))
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   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


----------------------------------------

(113) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   MARK(U42(0, x1)) -> c62(A__U42(0, x1), MARK(0))
   MARK(U42(nil, x1)) -> c62(A__U42(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(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


----------------------------------------

(115) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 4 trailing tuple parts
----------------------------------------

(116)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0) -> 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


----------------------------------------

(117) 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))

----------------------------------------

(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(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))
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   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


----------------------------------------

(119) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   MARK(U51(nil, x1, x2)) -> c65(A__U51(nil, x1, x2), MARK(nil))
   MARK(U51(0, x1, x2)) -> c65(A__U51(0, x1, x2), MARK(0))

----------------------------------------

(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(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))
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   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


----------------------------------------

(121) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 4 trailing tuple parts
----------------------------------------

(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(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)))
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   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


----------------------------------------

(123) 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))

----------------------------------------

(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(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)))
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   A__ISNATILIST(zeros) -> c34(A__U31(tt, zeros))
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   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)))
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   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


----------------------------------------

(125) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   MARK(U52(0, x1)) -> c66(A__U52(0, x1), MARK(0))
   MARK(U52(nil, x1)) -> c66(A__U52(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(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))
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   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


----------------------------------------

(127) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 4 trailing tuple parts
----------------------------------------

(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(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))
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   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


----------------------------------------

(129) 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))

----------------------------------------

(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(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)))
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   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


----------------------------------------

(131) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   MARK(U61(nil, x1)) -> c68(A__U61(nil, x1), MARK(nil))
   MARK(U61(0, x1)) -> c68(A__U61(0, x1), MARK(0))

----------------------------------------

(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(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))
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   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


----------------------------------------

(133) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 4 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(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))
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   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)))
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)))
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   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


----------------------------------------

(135) 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))

----------------------------------------

(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(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)))
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   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)))
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   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


----------------------------------------

(137) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing nodes:
   MARK(length(nil)) -> c69(A__LENGTH(nil), MARK(nil))
   MARK(length(tt)) -> c69(A__LENGTH(tt), MARK(tt))
   MARK(length(0)) -> c69(A__LENGTH(0), MARK(0))

----------------------------------------

(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(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)))
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   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)))
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   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


----------------------------------------

(139) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(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(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)))
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   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)))
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   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


----------------------------------------

(141) 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))

----------------------------------------

(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, 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))
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   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)))
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   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))
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


----------------------------------------

(143) 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))

----------------------------------------

(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, 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)))
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   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)))
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   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


----------------------------------------

(145) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 4 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, 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)))
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))
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   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


----------------------------------------

(147) 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)))

----------------------------------------

(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, 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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   MARK(U21(U61(z0, z1), x1)) -> c56(A__U21(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1)))
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   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)))
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   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


----------------------------------------

(149) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 1 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, 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)))
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   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)))
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   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


----------------------------------------

(151) 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)))

----------------------------------------

(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, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(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))
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   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)))
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)))
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   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


----------------------------------------

(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, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(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)))
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   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)))
   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)))
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   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


----------------------------------------

(155) 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)))

----------------------------------------

(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, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(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)))
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   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)))
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   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


----------------------------------------

(157) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 1 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, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(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)))
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   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)))
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   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)))
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


----------------------------------------

(159) 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)))

----------------------------------------

(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, 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)))
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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(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)))
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   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


----------------------------------------

(161) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 1 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, 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))
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   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))
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   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


----------------------------------------

(163) 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)))

----------------------------------------

(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, 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)))
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   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)))
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   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


----------------------------------------

(165) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 3 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, 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)))
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   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)))
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   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


----------------------------------------

(167) 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)))

----------------------------------------

(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))
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   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)))
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   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


----------------------------------------

(169) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 1 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, 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)))
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   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))
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   MARK(length(isNatList(z0))) -> c69(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
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   MARK(length(isNat(z0))) -> c69(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
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   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)))
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   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)))
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   A__U61(tt, U11(x0, z1)) -> c26(MARK(U11(x0, z1)))
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   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


----------------------------------------

(171) 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)))

----------------------------------------

(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, 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)))
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   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))
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   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


----------------------------------------

(173) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 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, 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)))
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   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)))
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))
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   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


----------------------------------------

(175) 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)))

----------------------------------------

(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, 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)))
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   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)))
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   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


----------------------------------------

(177) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 3 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, 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)))
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   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)))
   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)))
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   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)))
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, 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)))

----------------------------------------

(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, 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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   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)))
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   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


----------------------------------------

(181) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 1 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, 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)))
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   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))
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   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


----------------------------------------

(183) 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)))

----------------------------------------

(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, 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)))
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   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))
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   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


----------------------------------------

(185) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(186)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0) -> 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)))
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   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)))
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   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)))
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, 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)))

----------------------------------------

(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, 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)))
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   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), 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))
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   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


----------------------------------------

(189) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 3 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, 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))
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   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)))
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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)))
   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


----------------------------------------

(191) 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)))

----------------------------------------

(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, 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)))
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   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)))
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)))
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   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


----------------------------------------

(193) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 1 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))
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   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)))
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   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


----------------------------------------

(195) 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)))

----------------------------------------

(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, 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)))
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   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)))
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   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


----------------------------------------

(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, 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)))
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   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
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   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
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   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)))
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   A__U61(tt, U12(x0)) -> c26(MARK(U12(x0)))
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   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)))
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   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)))
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   A__U61(tt, U21(U32(z0), x1)) -> c26(A__LENGTH(a__U21(a__U32(mark(z0)), x1)), MARK(U21(U32(z0), x1)))
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   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))))
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   A__U61(tt, U22(U31(z0, z1))) -> c26(A__LENGTH(a__U22(a__U31(mark(z0), z1))), MARK(U22(U31(z0, z1))))
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   A__U61(tt, U22(U42(z0, z1))) -> c26(A__LENGTH(a__U22(a__U42(mark(z0), z1))), MARK(U22(U42(z0, z1))))
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   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)))
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)))
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   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(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


----------------------------------------

(199) 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)))

----------------------------------------

(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, 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)))
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   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))
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   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)))
   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


----------------------------------------

(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, 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)))
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   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))))
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   A__U61(tt, U12(x0)) -> c26(MARK(U12(x0)))
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   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)))
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   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)))
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   A__U61(tt, U21(U32(z0), x1)) -> c26(A__LENGTH(a__U21(a__U32(mark(z0)), x1)), MARK(U21(U32(z0), x1)))
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   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)))
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   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))))
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   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))))
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   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))))
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   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)))
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)))
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   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)))
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, 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)))

----------------------------------------

(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, 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)))
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   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(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)))
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   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


----------------------------------------

(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, 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)))
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   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)))
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   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


----------------------------------------

(207) 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)))

----------------------------------------

(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, 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)))
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   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(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))
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   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


----------------------------------------

(209) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 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, 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)))
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   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)))
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))
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   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


----------------------------------------

(211) 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)))

----------------------------------------

(212)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0) -> 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)))
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   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)))
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   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


----------------------------------------

(213) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing tuple parts
----------------------------------------

(214)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0) -> 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)))
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   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)))
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)))
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   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


----------------------------------------

(215) 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)))

----------------------------------------

(216)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0) -> 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)))
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   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)))
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)))
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   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


----------------------------------------

(217) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing tuple parts
----------------------------------------

(218)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0) -> 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)))
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   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)))
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   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


----------------------------------------

(219) 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)))

----------------------------------------

(220)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0) -> 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))
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   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)))
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   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)))
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


----------------------------------------

(221) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing tuple parts
----------------------------------------

(222)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0) -> 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)))
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   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))
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   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


----------------------------------------

(223) 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)))

----------------------------------------

(224)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0) -> 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))
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   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)))
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   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(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


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(225) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing tuple parts
----------------------------------------

(226)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0) -> 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)))
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   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)))
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))
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   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


----------------------------------------

(227) RelTrsToWeightedTrsProof (UPPER BOUND(ID))
Transformed relative TRS to weighted TRS
----------------------------------------

(228)
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
----------------------------------------

(229) TypeInferenceProof (BOTH BOUNDS(ID, ID))
Infered types.
----------------------------------------

(230)
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
----------------------------------------

(231) 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

----------------------------------------

(232)
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
----------------------------------------

(233) NarrowingProof (BOTH BOUNDS(ID, ID))
Narrowed the inner basic terms of all right-hand sides by a single narrowing step.
----------------------------------------

(234)
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
----------------------------------------

(235) 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

----------------------------------------

(236)
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


----------------------------------------

(237) 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

----------------------------------------

(238)
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


----------------------------------------

(239) SimplificationProof (BOTH BOUNDS(ID, ID))
Simplified the RNTS by moving equalities from the constraints into the right-hand sides.
----------------------------------------

(240)
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


----------------------------------------

(241) 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

----------------------------------------

(242)
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
----------------------------------------

(243) 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

----------------------------------------

(244)
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.